JON 0. NEWMAN, Circuit Judge:
A picture of a frog with the second of its four unwebbed “fingers” extended in a manner evocative of a well known human gesture of insult has presented this Court with significant issues concerning First Amendment protections for commercial speech. The frog appears on labels that Bad Frog Brewery, Inc. (“Bad Frog”) sought permission to use on bottles of its beer products. The New York State Liquor Authority (“NYSLA” or “the Authority”) denied Bad Frog’s application.
Bad Frog appeals from the July 29, 1997, judgment of the District Court for the Northern District of New York (Frederic J. Scullin, Jr., Judge) granting summary judgment in favor of NYSLA and its three Commissioners and rejecting Bad Frog’s commercial free speech challenge to NYSLA’s decision. We conclude that the State’s prohibition of the labels from use in all circumstances does not materially advance its asserted interests in insulating children from vulgarity or promoting temperance, and is not narrowly tailored to the interest concerning children. We therefore reverse the judgment insofar as it denied Bad Frog’s federal claims for injunctive relief with respect to the disapproval of its labels. We affirm, on the ground of immunity, the dismissal of Bad Frog’s federal damage claims against the commissioner defendants, and affirm the dismissal of Bad Frog’s state law damage claims on the ground that novel and uncertain issues of state law render this an inappropriate case for the exercise of supplemental jurisdiction.
Background
Bad Frog is a Michigan corporation that manufactures and markets several different types of alcoholic beverages under its “Bad Frog” trademark. This action concerns labels used by the company in the marketing of Bad Frog Beer, Bad Frog Lemon Lager, and Bad Frog Malt Liquor. Each label prominently features an artist’s rendering of [91]*91a frog holding up its four-“fingered” right “hand,” with the back of the “hand” shown, the second “finger” extended, and the other three “fingers” slightly curled. The membranous webbing that connects the digits of a real frog’s foot is absent from the drawing, enhancing the prominence of the extended “finger.” Bad Frog does not dispute that the frog depicted in the label artwork is making the gesture generally known as “giving the finger” and that the gesture is widely regarded as an offensive insult, conveying a message that the company has characterized as “traditionally ... negative and nasty.”1 Versions of the label feature slogans such as “He just don’t care,” “An amphibian with an attitude,” “Turning bad into good,” and “The beer so good ... it’s bad.” Another slogan, originally used but now abandoned, was “He’s mean, green and obscene.”
Bad Frog’s labels have been approved for use by the Federal Bureau of Alcohol, Tobacco, and Firearms, and by authorities in at least 15 states and the District of Columbia, but have been rejected by authorities in New Jersey, Ohio, and Pennsylvania.
In May 1996, Bad Frog’s authorized New York distributor, Renaissance Beer Co., made an initial application to NYSLA for brand label approval and registration pursuant to section 107-a(4)(a) of New York’s Alcoholic Beverage Control Law. See N.Y. Aleo. Bev. Cont. Law § 107-a(4)(a) (McKinney 1987 & Supp.1997). NYSLA denied that application in July. Bad Frog filed a new application in August, resubmitting the prior labels and slogans, but omitting the label with the slogan “He’s mean, green and obscene,” a slogan the Authority had previously found rendered the entire label obscene. That slogan was replaced with a new slogan, “Turning bad into good.” The second application, like the first, included promotional material making the extravagant claim that the frog’s gesture, whatever its past meaning in other contexts, now means “I want a Bad Frog beer,” and that the company’s goal was to claim the gesture as its own and as a symbol of peace, solidarity, and good will.
In September 1996, NYSLA denied Bad Frog’s second application, finding Bad Frog’s contention as to the meaning of the frog’s gesture “ludicrous and disingenuous.” NYS-LA letter to Renaissance Beer Co. at 2 (Sept. 18, 1996) (“NYSLA Decision”). Explaining its rationale for the rejection, the Authority found that the label “encourages combative behavior” and that the gesture and the slogan, “He just don’t care,” placed close to and in larger type than a warning concerning potential health problems,
foster a defiance to the health warning on the label, entice underage drinkers, and invite the public not to heed conventional wisdom and to disobey standards of decorum.
Id. at 3. In addition, the Authority said that it
considered that approval of this label means that the label could appear in grocery and convenience stores, with obvious exposure on the shelf to children of tender age
id., and that it
is sensitive to and has concern as to [the label’s] adverse effects on such a youthful audience.
Id. Finally, the Authority said that it
has considered that within the state of New York, the gesture of “giving the finger” to someone, has the insulting meaning of “Fuck You,” or “Up Yours,” ... a confrontational, obscene gesture, known to lead to fights, shootings and homicides ... [,] concludes that the encouraged use of this gesture in licensed premises is akin to [92]*92yelling “fire” in a crowded theatre, ... [and] finds that to approve this admittedly obscene, provocative confrontational gesture, would not be conducive to proper regulation and control and would tend to adversely affect the health, safety and welfare of the People of the State of New York.
Id.
Bad Frog filed the present action in October 1996 and sought a preliminary injunction barring NYSLA from taking any steps to prohibit the sale of beer by Bad Frog under the controversial labels. The District Court denied the motion on the ground that Bad Frog had not established a likelihood of success on the merits. See Bad Frog Brewery, Inc. v. New York State Liquor Authority, No. 96-CV-1668, 1996 WL 705786 (N.D.N.Y. Dec. 5, 1996). The Court determined that NYSLA’s decision appeared to be a permissible restriction on commercial speech under Central Hudson Gas & Electric Corp. v. Public Service Commission, 447 U.S. 557, 100 S.Ct. 2343, 65 L.Ed.2d 341 (1980), and that Bad Frog’s state law claims appeared to be barred by the Eleventh Amendment.
The parties then filed cross motions for summary judgment, and the District Court granted NYSLA’s motion. See Bad Frog Brewery, Inc. v. New York State Liquor Authority, 973 F.Supp. 280 (N.D.N.Y.1997). The Court reiterated the views expressed in denying a preliminary injunction that the labels were commercial speech within the meaning of Central Hudson and that the first prong of Central Hudson was satisfied because the labels concerned a lawful activity and were not misleading. Id. at 282. Turning to the second prong of Central Hudson, the Court considered two interests, advanced by the State as substantial: (a) “promoting temperance and respect for the law” and (b) “protecting minors from profane advertising.” Id. at 283.
Assessing these interests under the third prong of Central Hudson, the Court ruled that the State had failed to show that the rejection of Bad Frog’s labels “directly and materially advances the substantial governmental interest in temperance and respect for the law.” Id. at 286. In reaching this conclusion the Court appears to have accepted Bad Frog’s contention that
marketing gimmicks for beer such as the “Budweiser Frogs,” “Spuds Mackenzie,” the “Bud-Ice Penguins,” and the “Red Dog” of Red Dog Beer ... virtually indistinguishable from the Plaintiffs frog ... promote intemperate behavior in the same way that the Defendants have alleged Plaintiffs label would ... [and therefore the] regulation of the Plaintiffs label will have no tangible effect on underage drinking or intemperate behavior in general.
However, the Court accepted the State’s contention that the label rejection would advance the governmental interest in protecting children from advertising that was “profane,” in the sense of “vulgar.” Id. at 285 (citing Webster’s II New Riverside Dictionary 559 (1984)). The Court acknowledged the State’s failure to present evidence to show that the label rejection would advance this interest, but ruled that such evidence was required in cases “where the interest advanced by the Government was only incidental or tangential to the government’s regulation of speech,” id. at 285 (citing 44. Liquormart, Inc. v. Rhode Island, 517 U.S. 484, --, 116 S.Ct. 1495, 1508-09, 134 L.Ed.2d 711 (1996); Rubin v. Coors Brewing Co., 514 U.S. 476, 487-88, 115 S.Ct. 1585, 1592, 131 L.Ed.2d 532 (1995); City of Cincinnati v. Discovery Network, Inc., 507 U.S. 410, 428, 113 S.Ct. 1505, 1516, 123 L.Ed.2d 99 (1993); Bolger v. Youngs Drug Products Corp., 463 U.S. 60, 73, 103 S.Ct. 2875, 2883-84, 77 L.Ed.2d 469 (1983)), but not in cases “where the link between the regulation and the government interest advanced is self evident,” 973 F.Supp. at 285 (citing Florida Bar v. Went for It, Inc., 515 U.S. 618, 625-27, 115 S.Ct. 2371, 2376-78, 132 L.Ed.2d 541 (1995); Posadas de Puerto Rico Associates v. Tourism Co., 478 U.S. 328, 341-42, 106 S.Ct. 2968, 2976-77, 92 L.Ed.2d 266 (1986)). The Court concluded that
common sense requires this Court to conclude that the prohibition of the use of the profane image on the label in question will necessarily limit the exposure of minors in [93]*93New York to that specific profane image. Thus, to that extent, the asserted government interest in protecting children from exposure to profane advertising is directly and materially advanced.
973 F.Supp. at 286.
Finally, the Court ruled that the fourth prong of Central Hudson — narrow tailoring — was met because other restrictions, such as point-of-sale location limitations would only limit exposure of youth to the labels, whereas rejection of the labels would “completely foreclose the possibility” of their being seen by youth. Id. at 287. The Court reasoned that a somewhat relaxed test of narrow tailoring was appropriate because Bad Frog’s labels conveyed only a “superficial aspect of commercial advertising of no value to the consumer in making an informed purchase,” id., unlike the more exacting tailoring required in cases like U Liquonnart and Rubin, where the material at issue conveyed significant consumer information.
The Court also rejected Bad Frog’s void-for-vagueness challenge, id. at 287-88, which is not renewed on appeal, and then declined to exercise supplemental jurisdiction over Bad Frog’s pendent state law claims pursuant to 28 U.S.C. § 1367(e)(3) (1994), id. at 288.
Discussion
I. New York’s Label Approval Regime and Pullman Abstention
Under New York’s Alcoholic Beverage Control Law, labels affixed to liquor, wine, and beer products sold in the State must be registered with and approved by NYSLA in advance of use. See N.Y. Alco. Bev. Cont. Law § 107-a(4)(a). The statute also empowers NYSLA to promulgate regulations “governing the labeling and offering” of alcoholic beverages, id. § 107-a(l), and directs that regulations “shall be calculated to prohibit deception of the consumer; to afford him adequate information as to quality and identity; and to achieve national uniformity in this field in so far as possible,” id. § 107-a(2).
Purporting to implement section 107-a, NYSLA promulgated regulations governing both advertising and labeling of alcoholic beverages. Signs displayed in the interior of premises licensed to sell alcoholic beverages shall not contain “any statement, design, device, matter or representation which is obscene or indecent or which is obnoxious or offensive to the commonly and generally accepted standard of fitness and good taste” or “any illustration which is not dignified, modest and in good taste.” N.Y. Comp.Codes R. & Regs. tit. ix § 83.3 (1996). Labels on containers of alcoholic beverages “shall not contain any statement or representation, irrespective of truth or falsity, which, in the judgment of [NYSLA], would tend to deceive the consumer.” Id. § 84.1(e).
NYSLA’s actions raise at least three uncertain issues of state law. First, there is some doubt as to whether section 83.3 of the regulations, concerning designs that are not “in good taste,” is authorized by a statute requiring that regulations shall be calculated to prohibit deception of consumers, increase the flow of truthful information, and/or promote national uniformity. It is questionable whether a restriction on offensive labels serves any of these statutory goals. Second, there is some doubt as to whether it was appropriate for NYSLA to apply section 83.3, a regulation governing interior signage, to a product label, especially since the regulations appear to establish separate sets of rules for interior signage and labels. Third, there is some doubt as to whether section 84.1(e) of the regulations, applicable explicitly to labels, authorizes NYSLA to prohibit labels for any reason other than their tendency to deceive consumers.
It is well settled that federal courts may not grant declaratory or injunctive relief against a state agency based on violations of state law. See Pennhurst State School and Hospital v. Halderman, 465 U.S. 89, 106, 104 S.Ct. 900, 911, 79 L.Ed.2d 67 (1984). “The scope of authority of a state agency is a question of state law and not within the jurisdiction of federal courts.” Allen v. Cuomo, 100 F.3d 253, 260 (2d Cir.1996) (citing Pennhurst). Moreover, where a federal constitutional claim turns on an uncertain issue of state law and the controlling state statute is susceptible to an interpretation that would avoid or modify the federal consti[94]*94tutional question presented, abstention may be appropriate pursuant to the doctrine articulated in Railroad Commission v. Pullman Co., 312 U.S. 496, 61 S.Ct. 643, 85 L.Ed. 971 (1941). See Ohio Bureau of Employment Services v. Hodory, 431 U.S. 471, 477, 97 S.Ct. 1898, 1902-03, 52 L.Ed.2d 513 (1977); Planned Parenthood of Dutchess-Ulster, Inc. v. Steinhaus, 60 F.3d 122, 126 (2d Cir.1995). Were a state court to decide that NYSLA was not authorized to promulgate decency regulations, or that NYSLA erred in applying a regulation purporting to govern interior signs to bottle labels, or that the label regulation applies only to misleading labels, it might become unnecessary for this Court to decide whether NYSLA’s actions violate Bad Frog’s First Amendment rights.
However, we have observed that abstention is reserved for “very unusual or exceptional circumstances,” Williams v. Lambert, 46 F.3d 1275, 1281 (2d Cir.1995). In the context of First Amendment claims, Pullman abstention has generally been disfavored where state statutes have been subjected to facial challenges, see Dombrowski v. Pfister, 380 U.S. 479, 489-90, 85 S.Ct. 1116, 1122-23, 14 L.Ed.2d 22 (1965); see also City of Houston v. Hill, 482 U.S. 451, 467, 107 S.Ct. 2502, 2512-13, 96 L.Ed.2d 398 (1987). Even where such abstention has been required, despite a claim of facial invalidity, see Babbitt v. United Farm Workers National Union, 442 U.S. 289, 307-12, 99 S.Ct. 2301, 2313-16, 60 L.Ed.2d 895 (1979), the plaintiffs, unlike Bad Frog, were not challenging the application of state law to prohibit a specific example of allegedly protected expression. If abstention is normally unwarranted where an allegedly overbroad state statute, challenged facially, will inhibit allegedly protected speech, it is even less appropriate here, where such speech has been specifically prohibited. Abstention would risk substantial delay while Bad Frog litigated its state law issues in the state courts. See Zwickler v. Koota, 389 U.S. 241, 252, 88 S.Ct. 391, 397-98, 19 L.Ed.2d 444 (1967); Baggett v. Bullitt, 377 U.S. 360, 378-79, 84 S.Ct. 1316, 1326-27, 12 L.Ed.2d 377 (1964).
II. Commercial or Noncommercial Speech?
Bad Frog contends directly and NYS-LA contends obliquely that Bad Frog’s labels do not constitute commercial speech, but their common contentions lead them to entirely different conclusions. In Bad Frog’s view, the commercial speech that receives reduced First Amendment protection is expression that conveys commercial information. The frog labels, it contends, do not purport to convey such information, but instead communicate only a “joke,”2 Brief for Appellant at 12 n. 5. As such, the argument continues, the labels enjoy full First Amendment protection, rather than the somewhat reduced protection accorded commercial speech.
NYSLA shares Bad Frog’s premise that “the speech at issue conveys no useful consumer information,” but concludes from this premise that “it was reasonable for [NYSLA] to question whether the speech enjoys any First Amendment protection whatsoever.” Brief for Appellees at 24-25 n. 5. Ultimately, however, NYSLA agrees with the District Court that the labels enjoy some First Amendment protection, but are to be assessed by the somewhat reduced standards applicable to commercial speech.
The parties’ differing views as to the degree of First Amendment protection to which Bad Frog’s labels are entitled, if any, stem from doctrinal uncertainties left in the wake of Supreme Court decisions from which the modern commercial speech doctrine has evolved. In particular, these decisions have created some uncertainty as to the degree of protection for commercial advertising that lacks precise informational content.
[95]*95In 1942, the Court was “clear that the Constitution imposes no [First Amendment] restraint on government as respects purely commercial advertising.” Valentine v. Chrestensen, 316 U.S. 52, 54, 62 S.Ct. 920, 921, 86 L.Ed. 1262 (1942). In Chrestensen, the Court sustained the validity of an ordinance banning the distribution on public streets of handbills advertising a tour of a submarine. Twenty-two years later, in New York Times Co. v. Sullivan, 376 U.S. 254, 84 S.Ct. 710, 11 L.Ed.2d 686 (1964), the Court characterized Chrestensen as resting on “the factual conclusion^ that the handbill was ‘purely commercial advertising,’ ” id. at 266, 84 S.Ct. at 718 (quoting Chrestensen, 316 U.S. at 54, 62 S.Ct. at 921), and noted that Chrestensen itself had “reaffirmed the constitutional protection for ‘the freedom of communicating information and disseminating opinion,’ ” id. at 265-66, 84 S.Ct. at 718 (quoting Chrestensen, 316 U.S. at 54, 62 S.Ct. at 921) (emphasis added). The famously protected advertisement for the Committee to Defend Martin Luther King was distinguished from the unprotected Chrestensen handbill:
The publication here was not a “commercial” advertisement in the sense in which the word was used in Chrestensen. It communicated information, expressed opinion, recited grievances, protested claimed abuses, and sought financial support on behalf of a movement whose existence and objectives are matters of the highest public interest and concern.
Id. at 266, 84 S.Ct. at 718 (emphasis added). The implication of this distinction between the King Committee advertisement and the submarine tour handbill was that the handbill’s solicitation of customers for the tour was not “information” entitled to First Amendment protection.
In 1973, the Court referred to Chrestensen as supporting the argument that “commercial speech [is] unprotected by the First Amendment.” Pittsburgh Press Co. v. Pittsburgh Commission on Human Relations, 413 U.S. 376, 384, 93 S.Ct. 2553, 2558, 37 L.Ed.2d 669 (1973). Pittsburgh Press also endeavored to give content to the then “unprotected” category of “commercial speech” by noting that “[t]he critical feature of the advertisement in Valentine v. Chrestensen was that, in the Court’s view, it did no more than propose a commercial transaction.” Id. at 385, 93 S.Ct. at 2558. Similarly, the gender-separate help-wanted ads in Pittsburgh Press were regarded as “no more than a proposal of possible employment,” which rendered them “classic examples of commercial speech.” Id. The Court rejected the newspaper’s argument that commercial speech should receive some degree of First Amendment protection, concluding that the contention was unpersuasive where the commercial activity was illegal. See id. at 388-89, 93 S.Ct. at 2560-61.
Just two years later, Chrestensen was relegated to a decision upholding only the “manner in which commercial advertising could be distributed.” Bigelow v. Virginia, 421 U.S. 809, 819, 95 S.Ct. 2222, 2231, 44 L.Ed.2d 600 (1975) (emphasis added). Bigelow somewhat generously read Pittsburgh Press as “indi-eat[ing] that the advertisements would have received some degree of First Amendment protection if the commercial proposal had been legal.” Id. at 821, 95 S.Ct. at 2232. However, in according protection to a newspaper advertisement for out-of-state abortion services, the Court was careful to note, that the protected ad “did more than simply propose a commercial transaction.” Id. at 822, 95 S.Ct. at 2232. Though it was now clear that some forms of commercial speech enjoyed some degree of First Amendment protection, it remained uncertain whether protection would be available for an ad that only “propose[d] a commercial transaction.”
That uncertainty was resolved just one year later in Virginia State Board of Pharmacy v. Virginia Citizens Consumer Council, 425 U.S. 748, 96 S.Ct. 1817, 48 L.Ed.2d 346 (1976). Framing the question as “whether speech which does ‘no more than propose a commercial transaction’ ... is so removed from [categories of expression enjoying First Amendment protection] that it lacks all protection,” id. at 762, 96 S.Ct. at 1825-26, the Court said, “Our answer is that it is not,” id. Though Virginia State Board interred the notion that “commercial speech” enjoyed no First Amendment protection, it arguably kept alive the idea that protection was avail[96]*96able only for commercial speech that conveyed information:
Advertising, however tasteless and excessive it sometimes may seem, is nonetheless dissemination of information as to who is producing and selling what product, for what reason, and at what price.
Id. at 765, 96 S.Ct. at 1827; see id. at 763, 96 S.Ct. at 1826-27 (emphasizing the “consumer’s interest in the free flow of commercial information”).
Supreme Court commercial speech cases upholding First Amendment protection since Virginia State Board have all involved the dissemination of information. See, e.g., 44 Liquormart, 517 U.S. 484, 116 S.Ct. 1495 (price of beer); Rubin, 514 U.S. 476, 115 S.Ct. 1585 (alcoholic content of beer); Central Hudson, 447 U.S. 557, 100 S.Ct. 2343 (benefits of using electricity); Bates v. State Bar of Arizona, 433 U.S. 350, 97 S.Ct. 2691, 53 L.Ed.2d 810 (1977) (availability of lawyer services); Linmark Associates, Inc. v. Willingboro, 431 U.S. 85, 97 S.Ct. 1614, 52 L.Ed.2d 155 (1977) (residential “for sale” signs). In the one case since Virginia State Board where First Amendment protection was sought for commercial speech that contained minimal information' — the trade name of an optometry business — the Court sustained a governmental prohibition. See Friedman v. Rogers, 440 U.S. 1, 99 S.Ct. 887, 59 L.Ed.2d 100 (1979). Acknowledging that a trade name “is used as part of a proposal of a commercial transaction,” id. at 11, 99 S.Ct. at 895, and “is a form of commercial speech,” id., the Court pointed out “[a] trade name conveys no information about the price and nature of the services offered by an optometrist until it acquires meaning over a period of time.... ” Id. at 12, 99 S.Ct. at 895. Moreover, the Court noted, “the factual information associated with trade names may be communicated freely and explicitly to the public,” id. at 16, 99 S.Ct. at 897, presumably through the type of informational advertising protected in Virginia State Board. The trade name prohibition was ultimately upheld because use of the trade name had permitted misleading practices, such as claiming standardized care, see id. at 14, 99 S.Ct. at 896, but the Court added that the prohibition was sustainable just because of the “opportunity” for misleading practices, see id. at 15, 99 S.Ct. at 896-97.
Prior to Friedman, it was arguable from language in Virginia State Board that a trademark would enjoy commercial speech protection since, “however tasteless,” its use is the “dissemination of information as to who is producing and selling what product....” 425 U.S. at 765, 96 S.Ct. at 1827. But the prohibition against trademark use in Friedman puts the matter in considerable doubt, unless Friedman is to be limited to trademarks that either have been used to mislead or have a clear potential to mislead. Since Friedman, the Supreme Court has not explicitly clarified whether commercial speech, such as a logo or a slogan that conveys no information, other than identifying the source of the product, but that serves, to some degree, to “propose a commercial transaction,” enjoys any First Amendment protection. The Court’s opinion in Posadas, however, points in favor of protection. Adjudicating a prohibition on some forms of casino advertising, the Court did not pause to inquire whether the advertising conveyed information. Instead, viewing the case as involving “the restriction of pure commercial speech which does ‘no more than propose a commercial transaction,’ ” Posadas, 478 U.S. at 340, 106 S.Ct. at 2976 (quoting Virginia State Board, 425 U.S. at 762, 96 S.Ct. at 1825-26), the Court applied the standards set forth in Central Hudson, see id.
Bad Frog’s label attempts to function, like a trademark, to identify the source of the product. The picture on a beer bottle of a frog behaving badly is reasonably to be understood as attempting to identify to consumers a product of the Bad Frog Brewery.3 In addition, the label serves to propose a commercial transaction. Though the label communicates no information beyond the source [97]*97of the product, we think that minimal information, conveyed in the context of a proposal of a commercial transaction, suffices to invoke the protections for commercial speech, articulated in Central Hudson.4
Even if its labels convey sufficient information concerning source of the product to warrant at least protection as commercial speech (rather than remain totally unprotected), Bad Frog contends that its labels deserve full First Amendment protection because their proposal of a commercial transaction is combined with what is claimed to be political, or at least societal, commentary.
The “core notion” of commercial speech includes “speech which does no more than propose a commercial transaction.” Bolger, 463 U.S. at 66, 103 S.Ct. at 2880 (citations and internal quotation marks omitted). Outside this so-called “core” lie various forms of speech that combine commercial and noncommercial elements. Whether a communication combining those elements is to be treated as commercial speech depends on factors such as whether the communication is an advertisement, whether the communication makes reference to a specific product, and whether the speaker has an economic motivation for the communication. See id. at 66-67, 103 S.Ct. at 2879-81. Bolger explained that while none of these factors alone would render the speech in question commercial, the presence of all three factors provides “strong support” for such a determination. Id.; see also New York State Association of Realtors, Inc. v. Shaffer, 27 F.3d 834, 840 (2d Cir.1994) (considering proper classification of speech combining commercial and noncommercial elements).
We are unpersuaded by Bad Frog’s attempt to separate the purported social commentary in the labels from the hawking of beer. Bad Frog’s labels meet the three criteria identified in Bolger: the labels are a form of advertising, identify a specific product, and serve the economic interest of the speaker. Moreover, the purported noncommercial message is not so “inextricably intertwined” with the commercial speech as to require a finding that the entire label must be treated as “pure” speech. See Board of Trustees of the State University of New York v. Fox, 492 U.S. 469, 474, 109 S.Ct. 3028, 3031, 106 L.Ed.2d 388 (1989). Even viewed generously, Bad Frog’s labels at most “link[ ] a product to a current debate,” Central Hudson, 447 U.S. at 563 n. 5, 100 S.Ct. at 2350 n. 5, which is not enough to convert a proposal for a commercial transaction into “pure” noncommercial speech, see id. Indeed, the Supreme Court considered and rejected a similar argument in Fox, when it determined that the discussion of the noncommercial topics of “how to be financially responsible and how to run an efficient home” in the course of a Tupperware demonstration did not take the demonstration out of the domain of commercial speech. See Fox, 492 U.S. at 473-74, 109 S.Ct. at 3030-31.
We thus assess the prohibition of Bad Frog’s labels under the commercial speech standards outlined in Central Hudson.
III. The Central Hudson Test
Central Hudson sets forth the analytical framework for assessing governmental restrictions on commercial speech:
At the outset, we must determine whether the expression is protected by the First Amendment. For commercial speech to come within that provision, it at least must concern lawful activity and not be misleading. Next, we ask whether the asserted government interest is substantial. If both inquiries yield positive answers, we must determine whether the regulation di[98]*98rectly advances the government interest asserted, and whether it is not more extensive than is necessary to serve that interest.
447 U.S. at 566, 100 S.Ct. at 2351. The last two steps in the analysis have been considered, somewhat in tandem, to determine if there is a sufficient “ ‘fit’ between the [regulator’s] ends and the means chosen to accomplish those ends.” Posadas, 478 U.S. at 341, 106 S.Ct. at 2977. The burden to establish that “reasonable fit” is on the governmental agency defending its regulation, see Discovery Network, 507 U.S. at 416, 113 S.Ct. at 1509-10, though the fit need not satisfy a least-restrictive-means standard, see Fox, 492 U.S. at 476-81, 109 S.Ct. at 3032-35.
A. Lawful Activity and Not Deceptive
We agree with the District Court that Bad Frog’s labels pass Central Hudson’s threshold requirement that the speech “must concern lawful activity and not be misleading.” See Bad Frog, 973 F.Supp. at 283 n. 4. The consumption of beer (at least by adults) is legal in New York, and the labels cannot be said to be deceptive, even if they are offensive. Indeed, although NYSLA argues that the labels convey no useful information, it concedes that “the commercial speech at issue ... may not be characterized as misleading or related to illegal activity.” Brief for Defendants-Appellees at 24.
B. Substantial State Interests
NYSLA advances two interests to support its asserted power to ban Bad Frog’s labels: (i) the State’s interest in “protecting children from vulgar and profane advertising,” and (ii) the State’s interest “in acting consistently to promote temperance, ie., the moderate and responsible use of alcohol among those above the legal drinking age and abstention among those below the legal drinking age.” Id. at 26.
Both of the asserted interests are “substantial” within the meaning of Central Hudson. States have “a compelling interest in protecting the physical and psychological well-being of minors,” and “[t]his interest extends to shielding minors from the influence of literature that is not obscene by adult standards.” Sable Communications of California, Inc. v. Federal Communications Commission, 492 U.S. 115, 126, 109 S.Ct. 2829, 2836-37, 106 L.Ed.2d 93 (1989); see also Reno v. American Civil Liberties Union,, U.S. -, , 117 S.Ct. 2329, 2346, 138 L.Ed.2d 874 (1997) (“[W]e have repeatedly recognized the governmental interest in protecting children from harmful materials.”).
The Supreme Court also has recognized that states have a substantial interest in regulating alcohol consumption. See, e.g., 44 Liquormart, 517 U.S. at-, 116 S.Ct. at 1509; Rubin, 514 U.S. at 485, 115 S.Ct. at 1591. We agree with the District Court that New York’s asserted concern for “temperance” is also a substantial state interest. See Bad Frog, 973 F.Supp. at 284.
C.Direct Advancement of the State Interest
To meet the “direct advancement” requirement, a state must demonstrate that “the harms it recites are real and that its restriction will in fact alleviate them to a material degree.” Edenfield v. Fane, 507 U.S. 761, 771, 113 S.Ct. 1792, 1800, 123 L.Ed.2d 543 (1993) (emphasis added). A restriction will fail this third part of the Central Hudson test if it “provides only ineffective or remote support for the government’s purpose.” Central Hudson, 447 U.S. at 564, 100 S.Ct. at 2350.5
(1) Advancing the interest in protecting children from vulgarity. Whether the prohibition of Bad Frog’s labels can be said to materially advance the state interest in protecting minors from vulgarity depends on the extent to which underinelusiveness of regulation is pertinent to the relevant inquiry. The [99]*99Supreme Court has made it clear in the commercial speech context that underinclu-siveness of regulation will not necessarily defeat a claim that a state interest has been materially advanced. Thus, in Metromedia, Inc. v. City of San Diego, 453 U.S. 490, 101 5.Ct. 2882, 69 L.Ed.2d 800 (1981), the Court upheld a prohibition of all offsite advertising, adopted to advance a state interest in traffic safety and esthetics, notwithstanding the absence of a prohibition of onsite advertising. See id. at 510-12, 101 S.Ct. at 2893-95 (plurality opinion). Though not a complete ban on outdoor advertising, the prohibition of all offsite advertising made a substantial contribution to the state interests in traffic safety and esthetics. In United States v. Edge Broadcasting Co., 509 U.S. 418, 113 S.Ct. 2696, 125 L.Ed.2d 345 (1993), the Court upheld a prohibition on broadcasting lottery information as applied to a broadcaster in a state that bars lotteries, notwithstanding the lottery information lawfully being broadcast by broadcasters in a neighboring state. Though this prohibition, like that in Me-tromedia, was not total, the record disclosed that the prohibition of broadcasting lottery information by North Carolina stations reduced the percentage of listening time carrying such material in the relevant area from 49 percent to 38 percent, see Edge Broadcasting, 509 U.S. at 432, 113 S.Ct. at 2706, a reduction the Court considered to have “significance,” id. at 433, 113 S.Ct. at 2706-07.6
On the other hand, a prohibition that makes only a minute contribution to the advancement of a state interest can hardly be considered to have advanced the interest “to a material degree.” Edenfield, 507 U.S. at 771, 113 S.Ct. at 1800. Thus, In Bolger, the Court invalidated a prohibition on mailing literature concerning contraceptives, alleged to support a governmental interest in aiding parents’ efforts to discuss birth control with their children, because the restriction “provides only the most limited incremental support for the interest asserted.” 463 U.S. at 73, 103 S.Ct. at 2884. In Linmark, a town’s prohibition of “For Sale” signs was invalidated in part on the ground that the record failed to indicate “that proscribing such signs will reduce public awareness of realty sales.” 431 U.S. at 96, 97 S.Ct. at 1620. In Rubin, the Government’s asserted interest in preventing alcoholic strength wars was held not to be significantly advanced by a prohibition on displaying alcoholic content on labels while permitting such displays in advertising (in the absence of state prohibitions). 514 U.S. at 488, 115 S.Ct. at 1592. Moreover, the Court noted that the asserted purpose was sought to be achieved by barring alcoholic content only from beer labels, while permitting such information on labels for distilled spirits and wine. See id.7
In the pending case, NYSLA endeavors to advance the state interest in preventing exposure of children to vulgar displays by taking only the limited step of barring such displays from the labels of alcoholic beverages. In view of the wide currency of vulgar displays throughout contemporary society, including comic books targeted directly at children,8 barring such displays from labels for alcoholic beverages cannot realistically be expected to reduce children’s exposure to such displays to any significant degree.
We appreciate that NYSLA has no authority to prohibit vulgar displays appearing beyond the marketing of alcoholic beverages, but a state may not avoid the criterion of materially advancing its interest by authorizing only one component of its regulatory [100]*100machinery to attack a narrow manifestation of a perceived problem. If New York decides to make a substantial effort to insulate children from vulgar displays in some significant sphere of activity, at least with respect to materials likely to be seen by children, NYSLA’s label prohibition might well be found to make a justifiable contribution to the material advancement of such an effort, but its currently isolated response to the perceived problem, applicable only to labels on a product that children cannot purchase, does not suffice. We do not mean that a state must attack a problem with a total effort or fail the third criterion of a valid commercial speech limitation. See Edge Broadcasting, 509 U.S. at 434, 113 S.Ct. at 2707 (“Nor do we require that the Government make progress on every front before it can make progress on any front.”). Our point is that a state must demonstrate that its commercial speech limitation is part of a substantial effort to advance a valid state interest, not merely the removal of a few grains of offensive sand from a beach of vulgarity.9
The, District Court ruled that the third criterion was met because the prohibition of Bad Frog’s labels indisputably achieved the result of keeping these labels from being seen by children. That approach takes too narrow a view of the third criterion. Under that approach, any regulation that makes any contribution to achieving a state objective would pass muster. Edenfield, however, requires that the regulation advance the state interest “in a material way.” The prohibition of “For Sale” signs in Linmark succeeded in keeping those signs from public view, but that limited prohibition was held not to advance the asserted interest in reducing public awareness of realty sales. The prohibition of alcoholic strength on labels in Rubin succeeded in keeping that information off of beer labels, but that limited prohibition was held not to advance the asserted interest in preventing strength wars since the information appeared on labels for other alcoholic beverages. The valid state interest here is not insulating children from these labels, or even insulating them from vulgar displays on labels for alcoholic beverages; it is insulating children from displays of vulgarity.
(2) Advancing the state interest in temperance. We agree with the District Court that NYSLA has not established that its rejection of Bad Frog’s application directly advances the state’s interest in “temperance.” See Bad Frog, 973 F.Supp. at 286.
NYSLA maintains that the raised finger gesture and the slogan “He just don’t care” urge consumers generally to defy authority and particularly to disregard the Surgeon General’s warning, which appears on the label next to the gesturing frog. See Brief for Defendants-Appellees at 30. NYSLA also contends that the frog appeals to youngsters and promotes underage drinking. See id.
The truth of these propositions is not so self-evident as to reheve the state of the burden of marshalling some empirical evidence to support its assumptions. All that is clear is that the gesture of “giving the finger” is offensive. Whether viewing that gesture on a beer label will encourage disregard of health warnings or encourage underage drinking remain matters of speculation.
NYSLA has not shown that its denial of Bad Frog’s application directly and materially advances either of its asserted state interests.
D. Narrow Tailoring
Central Hudson’s fourth criterion, sometimes referred to as “narrow tailoring,” Edge Broadcasting, 509 U.S. at 430, 113 S.Ct. at 2705; Fox, 492 U.S. at 480, 109 S.Ct. [101]*101at 3034-35 ( narrowly tailored)10, requires consideration of whether the prohibition is more extensive than necessary to serve the asserted state interest. Since NYSLA’s prohibition of Bad Frog’s labels has not been shown to make even an arguable advancement of the state interest in temperance, we consider here only whether the prohibition is more extensive than necessary to serve the asserted interest in insulating children from vulgarity.
In its most recent commercial speech decisions, the Supreme Court has placed renewed emphasis on the need for narrow tailoring of restrictions on commercial speech. In Liquormart, where retail liquor price advertising was banned to advance an asserted state interest in temperance, the Court noted that several less restrictive and equally effective measures were available to the state, including increased taxation, limits on purchases, and educational campaigns. See 517 U.S. at-, 116 S.Ct. at 1510. Similarly in Rubin, where display of alcoholic content on beer labels was banned to advance an asserted interest in preventing alcoholic strength wars, the Court pointed out “the availability of alternatives that would prove less intrusive to the First Amendment’s protections for commercial speech.” 514 U.S. at 491, 115 S.Ct. at 1594.
In this case, Bad Frog has suggested numerous less intrusive alternatives to advance the asserted state interest in protecting children from vulgarity, short of a complete statewide ban on its labels. Appellant suggests “the restriction of advertising to point-of-sale locations; limitations on billboard advertising; restrictions on over-the-air advertising; and segregation of the product in the store.” Appellant’s Brief at 39. Even if we were to assume that the state materially advances its asserted interest by shielding children from viewing the Bad Frog labels, it is plainly excessive to prohibit the labels from all use, including placement on bottles displayed in bars and taverns where parental supervision of children is to be expected. Moreover, to whatever extent NYSLA is concerned that children will be harmfully exposed to the Bad Frog labels when wandering without parental supervision around grocery and convenience stores where beer is sold, that concern could be less intrusively dealt with by placing restrictions on the permissible locations where the appellant’s products may be displayed within such stores. Or, with the labels permitted, restrictions might be imposed on placement of the frog illustration on the outside of six-packs or cases, sold in such stores.
NYSLA’s complete statewide ban on the use of Bad Frog’s labels lacks a “reasonable fit” with the state’s asserted interest in shielding minors from vulgarity, and NYSLA gave inadequate consideration to alternatives to this blanket suppression of commercial speech. Cf. Bolger, 463 U.S. at 73, 103 S.Ct. at 2883-84 (“[T]he government may not ‘reduce the adult population ... to reading only what is fit for children.’ ”) (quoting Butler v. Michigan, 352 U.S. 380, 383, 77 S.Ct. 524, 526, 1 L.Ed.2d 412 (1957)) (footnote omitted).
E. Relief
Since we conclude that NYSLA has unlawfully rejected Bad Frog’s application for approval of its labels, we face an initial issue concerning relief as to whether the matter should be remanded to the Authority for further consideration of Bad Frog’s application or whether the complaint’s request for an injunction barring prohibition of the labels should be granted.
NYSLA’s unconstitutional prohibition of Bad Frog’s labels has been in effect since September 1996. The duration of that prohibition weighs in favor of immediate relief. Despite the duration of the prohibition, if it were preventing the serious impairment of a state interest, we might well leave it in force while the Authority is afforded a further opportunity to attempt to fashion some regulation of Bad Frog’s labels that accords with First Amendment requirements. But this case presents no such threat of serious im[102]*102pairment of state interests. The possibility that some children in supermarkets might see a label depicting a frog displaying a well known gesture of insult, observable throughout contemporary society, does not remotely pose the sort of threat to their well-being that would justify maintenance of the prohibition pending further proceedings before NYSLA. We will therefore direct the District Court to enjoin NYSLA from rejecting Bad Frog’s label application, without prejudice to such further consideration and possible modification of Bad Frog’s authority to use its labels as New York may deem appropriate, consistent with this opinion.
Though we conclude that Bad Frog’s First Amendment challenge entitles it to equitable relief, we reject its claim for damages against the NYSLA commissioners in their individual capacities. The District Court’s decision upholding the denial of the application, though erroneous in our view, sufficiently demonstrates that it was reasonable for the commissioners to believe that they were entitled to reject the application, and they are consequently entitled to qualified immunity as a matter of law.
IV. State Law Claims
Bad Frog has asserted state law claims based on violations of the New York State Constitution and the Alcoholic Beverage Control Law. See Complaint ¶¶ 40-46. In its opinion denying Bad Frog’s request for a preliminary injunction, the District Court stated that Bad Frog’s state law claims appeared to be barred by the Eleventh Amendment. See Bad Frog, 1996 WL 705786, at *5. In its summary judgment opinion, however, the District Court declined to retain supplemental jurisdiction over the state law claims, see 28 U.S.C. § 1367(c)(3), after dismissing all federal claims. See Bad Frog, 973 F.Supp. at 288.
Contrary to the suggestion in the District Court’s preliminary injunction opinion, we think that at least some of Bad Frog’s state law claims are not barred by the Eleventh Amendment. The jurisdictional limitation recognized in Pennhurst does not apply to an individual capacity claim seeking damages against a state official, even if the claim is based on state law. See Ying Jing Gan v. City of New York, 996 F.2d 522, 529 (2d Cir.1993); Wilson v. UT Health Center, 973 F.2d 1263, 1271 (5th Cir.1992) (“Pennhurst and the Eleventh Amendment do not deprive federal courts of jurisdiction over state law claims against state officials strictly in their individual capacities.”). Bad Frog purports to sue the NYSLA commissioners in part in their individual capacities, and seeks damages for their alleged violations of state law. See Complaint ¶¶ 5-7 and “Demand for Judgment” ¶ (3).
Nevertheless, we think that this is an appropriate case for declining to exercise supplemental jurisdiction over these claims in view of the numerous novel and complex issues of state law they raise. See 28 U.S.C. § 1367(c)(1). As noted above, there is significant uncertainty as to whether NYSLA exceeded the scope of its statutory mandate in enacting a decency regulation and in applying to labels a regulation governing interior signs. Bad Frog’s claims for damages raise additional difficult issues such as whether the pertinent state constitutional and statutory provisions imply a private right of action for damages, and whether the commissioners might be entitled to state law immunity for their actions.
In the absence of First Amendment concerns, these uncertain state law issues would have provided a strong basis for Pullman abstention. Because First Amendment concerns for speech restriction during the pen-dency of a lawsuit are not implicated by Bad Frog’s claims for monetary relief, the interests of comity and federalism are best served by the presentation of these uncertain state law issues to a state court. We thus affirm the District Court’s dismissal of Bad Frog’s state law claims for damages, but do so in reliance on section 1367(e)(1) (permitting declination of supplemental jurisdiction over claim “that raises a novel or complex issue of State law”).
Conclusion
The judgment of the District Court is reversed, and the case is remanded for entry of judgment in favor of Bad Frog on its claim [103]*103for injunctive relief; the injunction shall prohibit NYSLA from rejecting Bad Frog’s label application, without prejudice to such further consideration and possible modification of Bad Frog’s authority to use its labels as New York may deem appropriate, consistent with this opinion. Dismissal of the federal law claim for damages against the NYSLA commissioners is affirmed on the ground of immunity. Dismissal of the state law claim for damages is affirmed pursuant to 28 U.S.C. § 1367(e)(1). Upon remand, the District Court shall consider the claim for attorney’s fees to the extent warranted with respect to the federal law equitable claim.