SOTOMAYOR, Circuit Judge:
Defendant-appellant Ancelmo Figueroa appeals from a judgment of conviction after a jury trial in the United States District Court for the Eastern District of New York (Nick-erson, ./.). Figueroa was convicted of: (1) conspiring to induce Hector Reyes, an illegal alien, to enter the United States in violation of 18 U.S.C. § 371; (2) inducing Reyes to reside in the United States in violation of 8 U.S.C. §§ 1324(a)(l)(A)(iv) and (B)(ii); (3) conspiring to permit Ramon Emelio Garcia, an alien excludable under 8 U.S.C. § 1182(a)(2) for a prior aggravated felony conviction, to enter the United States in violation of 8 U.S.C. § 1327; (4) aiding and assisting Garcia to enter the United States in violation of § 1327; and (5-6) two counts of aiding and abetting Geraldo Pereyra in the use of a fraudulently obtained green card in violation of 18 U.S.C. § 1546(a). Figueroa was sentenced to 41 months of imprisonment, which he is now serving, three years of supervised release, and a special assessment of $300. Figueroa appeals only his two § 1327 convictions.
The dispute at issue in this appeal turns on competing interpretations of the terms of § 1327. The then-enacted provision sets forth increased criminal penalties for “[a]ny person who knowingly aids or assists any alien excludable under Section 1182(a)(2) ... (insofar as an alien excludable under such section has been convicted of an aggravated felony) ... to enter the United States,” and for “[a]ny person who ... conspires with any person or persons to ... permit any such alien to enter the United States.” Figueroa reads these provisions as permitting a conviction only when a defendant assists or conspires to permit the entry of an alien who he knows to be excludable because of a prior aggravated felony conviction. In the alternative, Figueroa argues that the rule of lenity requires this result. The Government maintains, and the district court agreed, however, that it is sufficient to sustain a § 1327 conviction for a defendant to know only that an alien is excludable. We agree with the district court’s conclusion and we affirm the judgment of conviction.
BACKGROUND
The following facts are limited to the events pertinent to this appeal. Sometime prior to August 1995, government agents were advised that Ramon Emelio Garcia was planning to enter the United States illegally [113]*113on a specified American Airlines flight. After having served nearly three years of imprisonment for a New York State kidnapping conviction, Garcia had been deported to the Dominican Republic. This conviction rendered Garcia excludable from the United States under 8 U.S.C. § 1182(a)(2). In order to prevent his entry, the agents conducted a surveillance of the Immigration and Naturalization Service (“INS”) inspection area on August 26, 1995, the day that Garcia was to arrive.
Shortly after his landing at the John F. Kennedy International Airport, the agents observed Garcia looking for inspection booth number eleven. Figueroa, an INS inspector, manned this booth. The agents saw Figueroa remove his cap and signal to Garcia “like it’s all right.” When Garcia reached the booth, Figueroa allowed him through without substantive questioning, although Garcia had placed different names on his passport and customs declaration forms. The agents arrested Garcia shortly after he left the inspection area and brought charges against him for illegally entering the United States in violation of 8 U.S.C. § 1326. Figueroa was subsequently arrested and separately indicted.
Garcia cooperated with the Government and testified against Figueroa at trial. Garcia testified that after being deported to the Dominican Republic, he met Geraldo Perey-ra, who was also known as “Arnaldo” and “Rosendo Correa.” Pereyra was introduced to Garcia as someone who could help him enter the United States illegally. After obtaining both a passport and a flight ticket for Garcia, Pereyra drove him to the Santa Domingo Airport. Pereyra advised Garcia not to use his real name on his customs declaration form and to look for booth eleven, Figueroa’s booth, upon landing. In a videotaped deposition taken from the Dominican Republic, Pereyra testified that his nickname was “Ar-naldo,” that he and Figueroa had been friends for some time, and that he knew Figueroa was an INS inspector. Pereyra further testified that the two men had met with one another two or three times per year for the last several years. No evidence was presented at trial to suggest that either Per-eyra or Figueroa knew exactly why Garcia was excludable from the United States.
At the close of trial, over defense objections, the trial judge instructed the jury, in relevant part, as follows:
To prove the crime alleged in Count Four [i.e., violation of § 1327 by aiding and assisting Garcia’s entry into the United States], the government must establish, beyond a reasonable doubt, the following three elements:
First: That the specified person, Ramon Emilio Garcia, was an alien excludable under section 1182(a)(2) of Title 8 of the United States Code;
Second: That the defendant aided and assisted Ramon Emilio Garcia to enter the United States; and
Third, that the defendant engaged in such conduct, knowing that Garcia was ex-cludable.
(Tr. at 675.)1
After the jury returned a guilty verdict on two counts of violating § 1327 and four other counts, Figueroa submitted several post-trial motions. He moved to dismiss the § P1327 charges, arguing first, that the jury should have been required to find that he knew Garcia was excludable because of his prior aggravated felony conviction, and second, that the evidence at trial was insufficient to establish this knowledge. The district court denied all of Figueroa’s motions, explaining, in pertinent part, that:
It is highly unlikely that the law makers envisioned [§ 1327] as applying only to those learned in the law as to the specific crime that the assisted alien had committed or even as to the ground for exclusion. Congress simply provided that if one knew the alien being assisted to be ineligible to receive a visa and excludable, one takes the chance that he has committed the serious crimes to which section 1327 applies.
United States v. Figueroa, No. CR 95-823, 1998 WL 273020, at *3 (E.D.N.Y. Jan. 9, 1998). On appeal, Figueroa argues that the district court erred in this ruling and improp[114]*114erly charged the jury on the mens rea required for a § 1327 conviction. We disagree.
DISCUSSION
This appeal involves the question of what mental state a defendant must have in order to be convicted under 8 U.S.C. § 1327. The then-enacted statute provides that:
Any person who knowingly aids or assists any alien excludable under section 1182(a)(2) of this title (insofar as an alien excludable under such section has been convicted of an aggravated felony) or 1182(a)(3) of this title (other than subpara-graph (E) thereof) of this title to enter the United States, or who connives or conspires with any person or persons to allow, procure, or permit any such alien to enter the United States, shall be fined under Title 18, or imprisoned not more than 10 years, or both.2
Because Figueroa was convicted under the part of the statute dealing with aliens previously convicted of aggravated felonies, the precise issue in this case is how much a defendant must know in order to be convicted.
The question of what mental state is required for a § 1327 conviction turns on “construction of the statute and ... inference of the intent of Congress.” United States v. Balint, 258 U.S. 250, 253, 42 S.Ct. 301, 66 L.Ed. 604 (1922); see also Staples v. United States, 511 U.S. 600, 604-05, 114 S.Ct. 1793, 128 L.Ed.2d 608 (1994); Liparota v. United States, 471 U.S. 419, 423, 105 S.Ct. 2084, 85 L.Ed.2d 434 (1985). We review issues of statutory construction de novo, see United States v. Proyect, 989 F.2d 84, 87 (2d Cir.1993), and the language of a statute is our starting point in such inquiries, see Connecticut Nat’l Bank v. Germain, 503 U.S. 249, 253-54, 112 S.Ct. 1146, 117 L.Ed.2d 391 (1992).
By using the word “knowingly,” Congress chose to include some knowledge requirement for a conviction under § 1327.3 Unfortunately, the language of § 1327 does little to clarify just how far Congress intended this knowledge requirement to go. For example, § 1327 does not indicate whether the word “knowingly” was meant to modify only the verbs “aid or assist” or some or all of the characteristics of the alien described in the statute. With regard to the part of the statute at issue, the knowledge requirement might therefore plausibly be read to extend to any one or more of the following characteristics: that the person aided is (1) an alien, (2) an excludable alien, (3) an alien who is excludable under § 1182(a)(2),4 or (4) an [115]*115alien who is excludable under §§ 1182(a)(2) by virtue of an aggravated felony conviction. The language of this section also does little to suggest whether knowledge of excludability, if relevant, should be understood as knowledge of the facts or circumstances that make a given alien excludable, or as extending further to knowledge that those circumstances serve as grounds for exclusion under the law.5
Figueroa argues that the term “knowingly” should be read to modify all the elements of the crime, including the precise nature of the alien’s excludable status, because such a reading “comports with the ‘most natural grammatical reading’” of the statute given its punctuation. Brief for Appellant at 15 (quoting United States v. X-Citement Video, Inc., 513 U.S. 64, 68, 115 S.Ct. 464, 130 L.Ed.2d 372 (1994)). There are certainly eases in which grammar and punctuation suggest a clear answer to a question of statutory interpretation. In the case of statutes like this, however, where a mental state adverb can modify some or all of the remaining words in a sentence, neither grammar nor punctuation resolves the question of how much knowledge Congress intended to be sufficient for a conviction.6 See United States v. Morris, 928 F.2d 504, 507 (2d Cir.1991) (“[W]e have been advised that punctuation is not necessarily decisive in construing statutes ... and with many statutes, a mental state adverb adjacent to initial words has been applied to phrases or clauses appearing later in the statute without regard to the punctuation or structure of the statute.”) (citations omitted).
In approaching statutes like this, courts often discern congressional intent by reading the text in light of the legal principles that operate in the relevant area of the law. See United States v. United States Gypsum Co., 438 U.S. 422, 437, 98 S.Ct. 2864, 57 L.Ed.2d 854 (1978) (“Congress will be presumed to have legislated against the background of our traditional legal concepts.”); Morissette v. United States, 342 U.S. 246, 263, 72 S.Ct. 240, 96 L.Ed. 288 (1952) (“[AJbsence of contrary [congressional] direction may be taken as [expressing Congress’s] satisfaction with widely accepted definitions, not as a departure from them.”). In the criminal arena, there is, for example, a very strong presumption that some mental state is required for culpability. This requirement, which distinguishes those who perform acts knowingly, intentionally, or recklessly from those who perform them by accident or by mistake, is “as universal and persistent in mature systems of law as belief in freedom of the human will and a consequent ability and duty of the normal individual to choose between good and evil.” Morissette, 342 U.S. at 250, 72 S.Ct. 240.
Equally strong in this area is the presumption that for knowledge to suffice for criminal culpability, it should, at minimum, be extensive enough to attribute to the know-er a “guilty mind,” or knowledge that he or she is performing a wrongful act. See Staples, 511 U.S. at 614-15, 114 S.Ct. 1793 (re [116]*116jecting the Government’s position when “the Government’s construction of the statute potentially would impose criminal sanctions on a class of persons whose mental state — ignorance of the characteristics of weapons in their possession — makes their actions entirely innocent”). Absent clear congressional intent to the contrary, statutes defining federal crimes are thus normally read to contain a mens rea requirement that attaches to enough elements of the crime that together would be sufficient to constitute an act in violation of the law. See id. at 608-16, 114 S.Ct. 1793; see also Liparota, 471 U.S. at 426, 105 S.Ct. 2084 (“This construction is particularly appropriate where, as here, to interpret the statute otherwise would be to criminalize a broad range of apparently innocent conduct.”)
This principle of construction can be used to set a presumed floor to the knowledge requirement in § 1327. In many, if not most, circumstances, it is perfectly innocent to aid persons in entering the United States. It is also perfectly innocent to assist many aliens, such as lawful permanent residents. Because criminal statutes should be presumed to criminalize only conduct that is accompanied by a non-innocent state of mind, the knowledge requirement in § 1327 must extend beyond the fact that the person aided is an alien.
The Government maintains that knowledge of an alien’s excludability should be sufficient under § 1327, and cites for this proposition a long line of cases that determine the mental states required to violate “regulatory” or “public welfare” statutes. The Supreme Court discussed these statutes in United States v. Freed, 401 U.S. 601, 91 S.Ct. 1112, 28 L.Ed.2d 356 (1971), a ease that involved the question of what knowledge is required for conviction under a statute that made it unlawful for any person “ ‘to receive or possess a firearm which is not registered to him.’ ” Id. at 607, 91 S.Ct. 1112 (quoting 26 U.S.C. § 5861(d)). At issue in Freed was whether a defendant could be convicted with only the knowledge that he possessed a grenade (which was defined as a “firearm” under the Act) or whether the defendant must also know that the grenade was not registered to him. The Court reasoned that because hand grenades are “highly dangerous offensive weapons,” “one would hardly be surprised to learn that possession of hand grenades is not an innocent act.” Id. at 609, 91 S.Ct. 1112. The Court therefore held that a conviction under § 5861(d) required a defendant’s knowledge that he or she possessed a grenade but not an unregistered grenade.
Later, in Staples, 511 U.S. at 600, 114 S.Ct. 1793, the Supreme Court interpreted the very same statute with the aid of the public welfare doctrine and clarified that notice, rather than danger, is the touchstone of its analysis. This time, the Court confronted a situation in which the defendant knew that he was handling a gun, but lacked knowledge of the specific characteristics of the weapon that made it an automatic weapon. Under the Act, automatic weapons qualified as “firearms,” and so were subject to the registration requirement, while non- or semi-automatic weapons did not so qualify. Rather than treating guns like the hand grenades addressed under the same statute in Freed, however, the Court noted that “there is a long tradition of widespread lawful gun ownership by private individuals in this country.” Id. at 610, 91 S.Ct. 1112. The Court also pointed out that “[ejven dangerous items can, in. some cases, be so commonplace and generally available that we would not consider them to alert individuals to the likelihood of strict regulation.” Id. at 611, 91 S.Ct. 1112. Because of the “common experience that owning a gun is usually licit and blameless conduct,” id. at 613, 91 S.Ct. 1112, the Court held that the conviction before it could not stand absent a showing that the defendant knew of the modifications on his gun that rendered it an automatic weapon, see id. at 619-20, 114 S.Ct. 1793.
These Supreme Court cases stand for the proposition that absent congressional intent to the contrary, statutes defining public welfare offenses should be read to require only so much knowledge as is necessary to provide defendants with reasonable notification that their actions are subject to strict regulation. In such cases, Congress is presumed to have placed the burden on defendants who have received such notice to [117]*117“ascertain at [their] peril whether [their conduct] comes within the inhibition of the statute.” Balint, 258 U.S. at 254, 42 S.Ct. 301; cf. also United States v. Chin, 981 F.2d 1275, 1280 (D.C.Cir.1992) (Ginsburg, J.) (“Congress meant to impose on the drug dealer the burden of inquiry and the risk of misjudgment.”).
Figueroa points out that the Supreme Court originally formulated the public welfare doctrine in the context of items that were inherently dangerous, see, e.g., Freed, 401 U.S. at 609, 91 S.Ct. 1112 (hand grenades); United States v. Dotterweich, 320 U.S. 277, 282-83, 64 S.Ct. 134, 88 L.Ed. 48 (1943) (misbranded and adulterated drugs); Balint, 258 U.S. at 254, 42 S.Ct. 301 (narcotics), and he argues that aliens, even if excludable, are human beings and should not be compared with the sorts of noxious substances that gave rise to the public welfare doctrine. Although this position has some intuitive appeal, it fails to account for recent developments in the law.
The Supreme Court has recently applied the interpretive principles employed in the case of public welfare crimes to a broader class of federal criminal statutes. In X-Citement Video, 513 U.S. at 64, 115 S.Ct. 464, for example, the Court examined the scienter requirement for a conviction under 18 U.S.C. § 2252, which provided in relevant part that:
(a) Any person who-
(1) knowingly transports or ships in interstate or foreign commerce by 'any means including by computer or mails, any visual depiction, if-
(A) the producing of such visual depiction involves the use of a minor engaging in sexually explicit conduct; and
(B) such visual depiction is of such conduct; shall be punished as provided in subsection (b) of this section.
The Court addressed the question of whether the term “knowingly” in subsection (1) modifies only the verbs “transports” and “ships” from that same subsection, or also the phrase “the use of a minor,” which appears in subsection (1)(A). See X-Citement Video, 513 U.S. at 68, 115 S.Ct. 464. Although the Court found that “ § P2252 is not a public welfare offense,” it did not reject the proposition that scienter requirements should be presumed to stop once a defendant is put on notice that he is committing a non-innocent act. Id. at 71, 115 S.Ct. 464. Rather, the Court held that “Morissette, reinforced by Staples, instructs that the presumption in favor of a scienter requirement should apply to each of the statutory elements that criminalize otherwise innocent conduct.” Id. at 72, 115 S.Ct. 464. The Court thus determined the mental state required for a § 2252 conviction by finding “the crucial element separating legal innocence from wrongful conduct,” id. at 73, 115 S.Ct. 464, and held that this element was the age of the person depicted because “one would reasonably expect to be free from regulation when trafficking in [non-obscene] sexually explicit ... materials involving adults,” but not in sexually explicit materials involving minors, id.7
This Circuit has, in fact, adopted this same approach when interpreting federal criminal statutes that deal with non-dangerous substances. In United States v. LaPorta, 46 F.3d 152 (2d Cir.1994), for .example, we examined 18 U.S.C. § 1361, a statute that provided criminal penalties for anyone who “willfully injure[d] or committed] any depredation against any property of the United States.” The question arose in this case as to whether conviction under that statute required a showing that the defendant’s relevant mental state extended to the fact that the property he burned was owned by the government. After acknowledging the existence of Morissette’s principle favoring a scienter requirement, we held that this principle failed to raise a presumption that defendants should have specific knowledge of the government’s ownership because “[a]rson is hardly ‘otherwise innocent conduct’ ” and because “[n]o one harbors settled expecta[118]*118tions that he is free to burn the property of others.” La Porta, 46 F.3d at 158.
Similarly, in United States v. Cook, 76 F.3d 596 (4th Cir.1996), the Fourth Circuit examined 21 U.S.C. § 861(a), which stated in relevant part:
It shall be unlawful for any person at least eighteen years of age to knowingly and intentionally...
(2) employ, hire, [or] use ... a person under eighteen years of age to assist in avoiding detection or apprehension for any offense of this subchap-ter or subehapter II of this chapter by any Federal, State or local law enforcement official; or
(3) receive a controlled substance from a person under 18 years of age, other than an immediate family member, in violation of this subchapter or sub-chapter II of this chapter.
The defendant argued that his conviction should be vacated because he was convicted without a showing that he knew the age of the person from whom he received illicit substances. The court rejected this contention, explaining in relevant part that “there is no reason to apply the presumption in favor of a knowledge requirement in this ease to protect otherwise innocent conduct for the obvious reason that receiving illegal drugs is not otherwise innocent conduct.” Cook, 76 F.3d at 601. Because § 861(a) is not now before us, we express no opinion as to whether the Fourth Circuit’s final interpretation of § 861(a) was correct in light of its language, legislative history, and larger statutory context. The Fourth Circuit’s approach is, nevertheless, instructive.
In fact, even before the Supreme Court’s decision in X-Citement Video, the Third Circuit in United States v. Hamilton, 456 F.2d 171 (3d Cir.1972) employed similar reasoning-in examining 18 U.S.C. § 2423, which read in relevant part:
Whoever knowingly persuades, induces, entices, or coerces any woman or girl who has not attained her eighteenth birthday, to go from one place to another by common carrier, in interstate commerce ... with intent that she be induced or coerced to engage in prostitution, debauchery or other immoral practice, shall be fined not more than $10,000 or imprisoned not more than ten years, or both.
The court read this statute against 18 U.S.C. §§ 2421 and 2422, which provided somewhat lesser penalties for defendants who knowingly transported persons of any age in order to engage in these kinds of practices. See Hamilton, 456 F.2d at 172-73. Because these other provisions made it non-innocent to engage in the same sorts of practices, regardless of the transportees’ ages, the court read § 2423 as generating increased penalties if the person transported happened to be under eighteen. The court thus held that “knowledge that [a] girl is under eighteen years of age is not part of the proof requisite by the Government in order to sustain a conviction” Id. at 173.8
Applying the principle of construction discussed to the statute at hand, defendants can be found guilty under § 1327 provided they have sufficient knowledge to recognize that they have done something culpable. The district court instructed the jury that it could find Figueroa guilty if Garcia was an alien excludable under § 1182(a)(2) because of an aggravated felony conviction, if Figueroa aided Garcia’s entry into the country, and if Figueroa knew Garcia was excludable.9 This charge was consistent with the law because knowledge that an alien is excludable should put any reasonable person on notice that it would be illegal to aid that person’s entry into the country.
Section 1324 imposes up to five years’ imprisonment for any person who “encourages or induces an alien to come to, enter, or reside in the United States, knowing or in reckless disregard of the fact that such coming to, entry, or residence is or will be in violation of the law_” 8 U.S.C. § 1324(l)(A)(iv). Read in light of its larger [119]*119statutory scheme, § 1327 thus places persons who would otherwise violate § 1324 at an increased risk if they happen to aid an alien who is excludable because of a conviction for an aggravated felony. Cf. Chin, 981 F.2d at 1280 (warning against readings that would “invite blindness” by criminal actors to the specific features of the more serious crimes they might be committing). Section 1327 thereby generates incentives for § 1324 violators to find out whether they are assisting an alien felon into the country and to avoid aiding aliens in this narrow class.10
Of course, the above conclusions were derived from presumptions inherent in the criminal law, and these presumptions should only be used to determine legislative intent when Congress has been either silent or at least sufficiently unclear about the required mens rea that departure from these principles would be unwarranted. See Morissette, 342 U.S. at 263, 72 S.Ct. 240. Figueroa argues that a close examination of the legislative history surrounding § 1327 suggests that Congress intended to depart from these principles by establishing a more specific knowledge requirement. Figueroa’s main support for this contention is Senator Chiles’s suggestion that the amendment to § 1327 at issue here was “directed at those persons in the United States — citizens or noncitizens — who actually recruit aliens in foreign countries for the purpose of dealing drugs in the United States and/or to assist such aliens in gaining illegal entry into this country.” 133 Cong. Ree. 8772 (daily ed. Apr. 9, 1987) (statement of Sen. Chiles). One other Senator made a similar remark. The classes of aided aliens to which the statute applies are, however, both over— and under-inclusive when compared to those discussed by 'Senator Chiles because § 1327 allows for the entry of aliens recruited for drug dealing purposes, so long as they are not convicted aggravated felons, and excludes such felons, even if they are not entering for the purpose of drug sales or distribution. The principles of construction underlying the criminal law serve as much better signposts to congressional intent in these kinds of circumstances than a statute’s sparse and inconsistent legislative history. See In re Olga Coal Co., 159 F.3d 62, 67 (2d Cir.1998) (“ ‘[Isolated [floor] remarks are entitled to little or no weight’ in statutory interpretation.”) (quoting Murphy v. Empire of Am. FSA, 746 F.2d 931, 935 (2d Cir.1984) (second alteration in original)).
Figueroa’s reliance on the rule of lenity is, finally, also misplaced. The rule of lenity provides that ambiguities concerning legislative intent in criminal statutes should be resolved in favor of the accused. See Ratzlaf v. United States, 510 U.S. 135, 148, 114 S.Ct. 655, 126 L.Ed.2d 615 (1994). However, “[t]he rule is inapplicable unless ‘after a court has seize[d][on] every thing from which aid can be derived, it is still left with an ambigu[ity].’ ” United States v. Canales, 91 F.3d 363, 367-68 (2d Cir.1996) (quoting Chapman v. United States, 500 U.S. 453, 463, 111 S.Ct. 1919, 114 L.Ed.2d 524 (1991) (internal quotation marks and citation omitted) (alterations in original)). In the present case, we have been able to discern Congress’s intent by reading § 1327 in light of the background principles that operate in the criminal law. These principles leave none of the interpretive issues in this case open, and the rule of lenity is therefore inapplicable to our inquiry. See id.
CONCLUSION
For the reasons discussed, we hold that a defendant can be convicted under § 1327 for aiding an alien who is excludable because of a prior aggravated felony conviction if the defendant knows only that the alien is excluda-ble. Therefore, the district court’s charge to the jury was sufficient, and we affirm Figueroa’s judgment of conviction.