OPINION
TÁLLMAN, Circuit Judge:
Crime, Justice & ■ America, Inc. (“CJ&A”) appeals the entry of judgment in favor of Butte County Sheriff Kory Honea following a bench trial in CJ&A’s 42 U.S.C. § 1983 action against the'Sheriff. The Sheriff oversees operation of the Butte County Jail, which prohibits delivery of unsolicited commercial mail to inmates. CJ&A publishes a magazine aimed at county jail inmates and argues that the jail’s mail policy violates the First Amendment. !
Based on the evidence presented at trial, the district court found the policy justified by legitimate penological interests. It also determined that electronic distribution of the magazine at recently installed kiosks was an adequate substitute for regular distribution of paper copies, which would have introduced thousands of pages of unsolicited paper into a facility where inmates habitually misuse paper in ways that threaten institutional security. Because the policy is reasonably related to a valid penological interest, the district court held the policy does not violate the First Amendment and granted judgment for the Sheriff.
I
A
Crime, Justice & America (“the magazine”) contains articles intended to help inmates navigate the criminal justice system, as well as advertisements for attorneys and bail bondsmen. CJ&A provides the magazine to inmates for free; it does not offer subscriptions. Its only source of revenue is the advertising it sells.
CJ&A distributes its magazine in one of two ways. In jails that allow “general distribution,” stacks of the magazine are left in common areas each week. In other jails, copies of the magazine are individually addressed and mailed to one out of every ten inmates, using, publicly available inmate roster information.
B
The Butte County Jail in Oroville, California, houses an average of 580-590 inmates each day. Due to staffing constraints, inmates are not directly supervised by a correctional officer for significant portions of the day.- The- jail instead employs “remote surveillance,, direct observation” and “linear” models of supervision, so corrections officers spend just a few minutes of every hour in each housing area, or briefly -observe inmates from hallways without even entering housing areas. That means corrections officers are not physically present in all areas of the jail to continually monitor inmate behavior.
Abuse of paper is a persistent problem at the, Butte County Jail. Inmates use paper to cover windows, speakers, and lights; to clog toilets and block air vents; to start fires; and to conceal contraband. Jail officials report that paper-related violations occur “every day.” These violations are almost always committed using paper with which inmates do not have a personal connection, such as pages torn out of phone books or donated paperbacks. Correctional supervisors testified that “personally owned papers” such as letters, photographs, and legal mail are almost never used for such purposes.
In an effort to combat paper-related violations, thirty-one electronic kiosks were installed throughout the jail in' 2014, along with two portable kiosks. The kiosks allow inmates to access electronic versions of the jail handbook, administrative forms, and reading material. The kiosks can easily accommodate reading material uploaded in portable document format (“PDF”).
C
In 2004, CJ&A requested permission to distribute 50-55 paper copies of its magazine at Butte County Jail every week. Each issue of the magazine has 36-r40 pages, so granting CJ&A’s request would have resulted in the introduction to the facility of'at least 1,800 pages’ worth of material every week. Butte : County officials refused CJ&A’s request, citing a longstanding but unpublished policy forbidding the delivery of unsolicited commercial mail to inmates. The month after CJ&A made its request, Butte County issued a departmental order that put this policy into writing.
CJ&A corresponded with Butte County officials for several years, trying unsuccessfully to convince them to distribute the magazine. In 2008, CJ&A filed a civil rights suit against the Butte County Sheriff in the Eastern District of California, arguing that the jail’s ban on unsolicited commercial mail violates the First Amendment. The district court entered summary judgment for the Sheriff. CJ&A appealed and a prior panel of our Court reversed and remanded, holding that questions of material fact precluded summary judgment. Hrdlicka v. Reniff, 631 F.3d 1044, 1046 (9th Cir. 2011), reh’g en banc denied, 656 F.3d 942 (9th Cir. 2011), cert. denied sub. nom. Reniff v. Hrdlicka, 565 U.S. 1197, 132 S.Ct. 1544, 182 L.Ed.2d 164 (2012).
The district ’court conducted a four-day bench trial in November 2014. During the trial, jail officials testified that they would permit PDF versions of the magazine to be made available on the electronic kiosks they had recently installed, but the kiosks were not properly working at the time. In February 2015, while the case was still under submission awaiting the court’s decision, the Sheriff moved to reopen the case and proffered Jail Operations Commander Captain Jerry Jones’s declaration that “the kiosks/monitors ... [were] now fully operational.” CJ&A objected, but the district court granted the motion and admitted the Jones declaration into evidence.
In May 2015, the district court rendered its judgment in favor of the Sheriff, holding that the jail’s mail policy did not violate the First Amendment and denying CJ&A’s claims for declaratory and injunctive relief. CJ&A appealed. It also filed.a motion for an Order Indicating Willingness to Entertain a Motion to Re-Open Discovery, or in the alternative a Motion for Relief from Judgment and to Re-Open Discovery, arguing that it should .be permitted to conduct discovery regarding the kiosks. The district court denied the motion, an,d CJ&A appealed that-ruling.
We consolidated both appeals and we have jurisdiction pursuant to 28 U.S.C. § 1291. We affirm.
We review de novo the constitutionality of Butte County’s mail policy, “the district court’s conclusions of law, and its determinations on mixed questions of law and fact.” Cal. First Amendment Coal. v. Woodford, 299 F.3d 868, 872-73 (9th Cir. 2002). The district court’s underlying factual findings are reviewed for clear.error, and we “will not disturb those findings without a ‘definite and firm conviction that a mistake has been committed.’ ” Id. at 873 (quoting Jones v. United States, 127 F.3d 1154, 1156 (9th Cir. 1997)).
Ill
The Sheriff initially argued that Butte County’s mail policy does not impinge on inmates’ constitutional rights at all because “the First Amendment does not protect distribution of a publication to inmates who have not requested it.” Hrdlicka, 631 F.3d at 1048. We rejected that argument in Hrdlicka, holding that “publishers and inmates have a First Amendment interest in communicating with each other,” whether that communication is solicited or not. Id. at 1049. Therefore, Butte County’s mail policy should be evaluated under the test ■.established for reviewing constitutional challenges to prison regulations in Turner v. Safley, 482 U.S. 78, 107 S.Ct. 2254, 96 L.Ed.2d 64 (1987). Id.
In Turner, the Supreme Court acknowledged that “[rjunning a prison is an inordinately difficult undertaking that requires expertise, planning, and the commitment of resources, all of which aré peculiarly within the province of the legislative and executive branches of government.” 482 U.S. at 84-85, 107 S.Ct. 2254. It sought “to formulate a standard of review for prisoners’ constitutional claims that is responsive both to the ‘policy of judicial restraint regarding prisoner complaints and [to] the need to protect constitutional rights.’ ” Id. at 85, 107 S.Ct. 2254 (quoting Procunier v. Martinez, 416 U.S. 396, 406, 94 S.Ct. 1800, 40 L.Ed.2d 224 (1974), rev’d on other grounds, Thornburgh v. Abbott, 490 U.S. 401, 413-14, 109 S.Ct. 1874, 104 L.Ed.2d 459 (1989)).
The Court concluded that “when a prison regulation impinges on inmates’ constitutional rights, the regulation is valid if it is reasonably related to legitimate penological interests.” Id. at 89-90, 107 S.Ct. 2254. It laid out a four-factor test for evaluating the reasonableness of regulations, which requires courts to consider (1) whether there is a “rational. connection” between the regulation and a “legitimate and neutral” government objective; (2) whether “alternative means of exercising the right” remain available to inmates; (3) “the impact accommodation of the asserted constitutional right will have on guards and other inmates, and on the allocation of prison resources;” and (4) whether “the existence of obvious, easy alternatives” to the regulation indicate that it “is an ‘exaggerated response’ to prison concerns.” Id. (citation omitted).
For the reasons explained below, we conclude that the evidence supports the district court’s conclusion that the Turner factors favor the Sheriff, and that Butte County’s ban on unsolicited commercial mail therefore does not violate the First Amendment. The trial court faithfully adhered to the Turner analysis in evaluating the record before it.
Under Turner, the first question We ask is whether there is a “ ‘valid, rational connection’ between the prison regulation and the legitimate governmental interest put forward to justify it.” Id. at 89, 107 S.Ct. 2254 (quoting Block v. Rutherford, 468 U.S. 576, 586, 104 S.Ct. 3227, 82 L.Ed.2d 438 (1984)). A policy “cannot be sustained where the logical connection between the regulation and the asserted goal is so remote as to render the policy arbitrary or irrational.” Id. at 89-90, 107 S.Ct. 2254. The government’s objective must be “legitimate and neutral,” id. at 90, 107 S.Ct. 2254, meaning it “must further an important or substantial governmental interest unrelated to the suppression of expression,” Thornburgh, 490 U.S. at 415, 109 S.Ct. 1874. The first factor “is a sine qua non: ‘[I]f the prison fails to show that the regulation is rationally related to a legitimate penological objective, we do not consider the other factors.’ ” Hrdlicka, 631 F.3d at 1051 (quoting Ashker v. Cal. Dep’t of Corr., 350 F.3d 917, 922 (9th Cir. 2003)).
The Sheriffs primary justification for the Butte County Jail mail policy is that it promotes jail security by reducing access to the type of paper that inmates are most likely to misuse. Relatedly, he argues that the policy conserves staff resources and prevents a flood of other unsolicited mail from entering the jail.
CJ&A does not argue that jail security and conservation of staff resources are not legitimate penological objectives; it argues that there is no rational relationship between those objectives and Butte County’s ban on unsolicited commercial mail.
It also contends that upholding the policy would contravene our jurisprudence regarding prisoners’ rights. CJ&A is mistaken for several reasons.
CJ&A argues that “[tjhere is no obvious, intuitive connection between banning delivery of unsolicited publications, or [the] magazine, and promoting jail security.” But even if the connection between the mail policy and jail security is not immediately obvious, the Sheriff presented evidence that ma<je the connection clear.
The district court found that inmates in the Butte County Jail use paper for a variety, of “nefarious acts,” including covering windows and lights, blocking air vents and speakers, clogging toilets, passing notes, obstructing security cameras, and hiding contraband. Covering windows and lights makes it difficult for corrections officers to perform required safety checks, and it allows inmates to conceal their activities. Blocking speakers prevents corrections officers and inmates from communicating with each other. The dangers associated with inmates using paper to obstruct security cameras and conceal contraband are self-evident.
The district court also found that inmates are far more likely to misuse paper with which they do not have a personal connection, such as pages torn from phone books or donated books, than paper that belongs to them, such as legal mail, personal letters, and photographs. Thus, the ban on unsolicited commercial mail is intended to limit inmates’ access to the type of paper they are most likely to use improperly to compromise jail security.
CJ&A argues that because we reversed summary judgment for the Sheriff in Hrdlicka, we cannot conclude now that he has established a rational relationship between the mail policy and jail security. But we did not hold.that the Sheriff could not possibly establish that there was a rational relationship, only that on the record before us then, “the degree to which allowing distribution of [the magazine] in the' jails would ... affect jail security” was “unclear.” Hrdlicka, 631 F.3d at 1052. Therefore, the Sheriff was not entitled to judgment as a matter of law at that time. Id. at 1055. This holding did not preclude the Sheriff from ultimately prevailing through supporting evidence adduced at trial.
The district court carefully considered trial evidence that was not before us in Hrdlicka. In Hrdlicka, Lieutenant Bryan Flicker and Capt. Jones, both Butte County corrections officers, only submitted declarations. At trial, the district court heard live testimony from Lt. Flicker and Capt. Jones, who provided more detailed information about the jail’s supervision models and the security problems posed by excess paper in the jail. Lt. Flicker explained that “remote surveillance, direct’ observation” and linear models of supervision give corrections officials less control over inmates’ behavior than other supervision models. Capt. Jones explained how covering lights, windows, and speakers' creates security hazards. Lt. Flicker testified that from 2010 to 2014, “about 3,400 rule violations involving paper products occurred,” arid he estimated that “99.9” percent of those violations involved generally available paper rather than “personally owned papers.” This evidence establishes that there is a rational relationship between'banning unsolicited commercial mail and jail security.
CJ&A asserts that upholding Butte County’s mail policy “would be out of sync with the court’s most applicable cases.” And it’s true that on several occasions, applying Turner, we have struck down prison regulations limiting.the types of mail inmates could receive. The crucial distinction is that in each of those cases, the defendants’ mail policies were arbitrary or insufficiently related to the asserted government interest.
In Prison Legal News v. Cook, inmates and the publisher of a non-profit prison newsletter challenged an Oregon' policy that prohibited the delivery of standard-rate mail to inmates, as it applied to “subscription non-profit organization mail.” 238 F.3d 1145, 1146 (9th Cir. 2001) (PLN I). State officials argued that the policy was intended to prevent contraband from entering the jail, minimize fire hazards, promote efficient cell searches, and- improve prison security. Id. at 1150-51. We held that none of these interests justified “tying the receipt of subscription non-profit newsletters to postal service rate classifications.” Id. at 1149-50.
Later that year, we struck down a similar regulation “as applied to pre-paid, for-profit* subscription publications.” Morrison v. Hall, 261 F.3d 896, 898 (9th Cir. 2001). The defendants -in Morrison offered similar justifications for their rule as the defendants in PLN I, and we rejected them for similar reasons, holding that “prohibiting inmates from receiving mail based on the postage rate at which the mail was sent is an arbitrary means of achieving the goal of volume control.” Id. at 902-904.
The regulation at issue in Morrison was deemed an “exaggerated response” because it “fail[ed] to distinguish between true ‘junk mail’ and subscriptions that have been both paid for and solicited by the inmates.” Id. at 905. But we noted that “prisons can and have adopted policies permitting prisoners to receive for-profit, commercial publications, while at the same time, prohibiting prisoners from receiving unsolicited junk mail.” Id, (emphasis added).
In Prison Legal News v. Lehman, we struck down a Washington regulation that prohibited receipt of “non-subscription bulk mail and catalogs” that had been requested by inmates. 397 F.3d 692, 695-96 (9th Cir. 2005) (PLN II). We agreed with the district court that “the ban on non-subscription bulk mail was not rationally related to a neutral government objective.” Id. at 699, 701. And we emphasized that we were not dealing with “a scenario in which a publisher has attempted to flood a facility with publications sent to all inmates, regardless of whether they requested the publication.” Id. at 701.
In each of these cases, there was an insufficient connection between the mail policy at issue and the asserted justification for it. But the Butte County Jail’s ban on unsolicited commercial mail is not an arbitrary form of volume control; it is a rational response to the fact that its inmates consistently misuse unsolicited paper in ways that threaten institutional security.
CJ&A also contends that because the Butte County Jail already has-rules governing paper in the jail, the ban on unsolicited commercial mail is irrational. Inmates may not keep more than a three-inch stack of non-legal paper in their cells, and they are not permitted to leave paper in common areas. Thus, CJ&A argues that its magazine could not increase clutter in cells or common areas.
We have taken these sorts of rules into account before. In Morrison, we stated that because the defendant prison system already “limit[ed] the total amount of property in a cell ... permitting inmates to receive for-profit, subscription publications could not possibly increase the total volume of cell materials.” 261 F.3d at 902. We used similar logic to . reject justifications of mail restrictions in PLN I. See 238 F.3d at 1150-51.
However, in those cases, prison officials’ rationales for limiting mail, such as reducing fire hazards and ensuring efficient cell searches, had more to do with the amount of paper in inmates’ cells than the type of paper. See id. The fact that, jail regulations already restricted the amount of paper inmates could have made restrictions on the type of mail unnecessary.
Here, however,- the Sheriffs justification-jail security—is tied to the type of paper inmates have access to, not the amount of it. Inmates are more likely to commit security violations using paper with which they have- no personal connection. Thus, a policy that forbids delivery of unsolicited commercial mail is rational, even if there are already limits on the amount of paper inmates can keep in their cells. , .. ..
Maintaining security in a jail is inarguably a legitimate government interest. See Thornburgh, 490 U.S. at 415, 109 S.Ct. 1874 (“[Pjrotecting prison security ... is central to all other corrections goals.” (internal quotation marks omitted)). Because the Sheriff presented extensive evidence regarding the security risks posed by paper, and the fact that generally available paper is most likely to be misused, he established that the ban on unsolicited commercial mail is rationally connected to a legitimate government interest. Therefore, the first Turner factor weighs in favor of the Sheriff.
The second Turner factor asks “whether there are alternative means of exercising the right that remain open to prison inmates.” 482 U.S. at 90, 107 S.Ct. 2254. “Where other avenues remain available for the exercise of the asserted right, courts should be particularly conscious of the measure of judicial deference owed to corrections officials ... in gauging the validity of the regulation.” Id. (internal citation and quotation marks omitted). These alternatives “need not be ideal, however; they need only be available.” Overton v. Bazzetta, 539 U.S. 126, 135, 123 S.Ct. 2162, 156 L.Ed.2d 162 (2003).
The district court considered two alternatives to distributing hard copies of CJ&A’s magazine to ten percent of Butte County inmates every week: the jail library and electronic kiosks. Jail officials offered to make two copies of the magazine available in the library, but the library can only be accessed by request, and only by about twenty-five inmates per day. Officials installed electronic kiosks throughout the jail during the litigation, and they testified that they could now load PDF versions of the magazine onto the kiosks. The district court found that the library alone was inadequate, but the kiosks constituted an adequate alternative.
The district court correctly found that the kiosks are an adequate alternative. With the kiosks in place, there are thirty-one locations throughout the jail where inmates could access an electronic version of the magazine, plus two portable kiosks.
This amounts to one kiosk for every eighteen inmates. Although the kiosks do not guarantee the same level of saturation as delivering fifty-five hard copies of the magazine to the jail every week, they do provide a meaningful way for CJ&A to offer its magazine to inmates. Turner does not require that the “alternative avenue” provide exactly the same level of communication as the plaintiffs preferred method, only that “other means of expression” be available. See Thornburgh, 490 U.S. at 417-18, 109 S.Ct. 1874. Thus, the second Turner factor weighs in favor of the Sheriff.
The third Turner factor requires us to consider “the impact accommodation of the asserted constitutional right will have on guards and other inmates, and on the allocation of prison resources generally.” 482 U.S. at 90, 107 S.Ct. 2254. “When accommodation of an asserted right will have a significant ‘ripple effect’ on fellow inmates or on prison staff, courts should be particularly deferential to the informed discretion of corrections officials.” Id.
The Sheriff argues that requiring the jail to distribute hard copies of the magazine would burden prison resources for two related reasons. First, “additional resources would be necessary to monitor and clean the large quantity of paper publications that would be added to the jail each week following [the magazine’s] delivery.”
Second, allowing distribution of CJ&A’s magazine could prompt other commercial publications to seek distribution in the jail, which would either require the jail to make content-based decisions about what should be delivered, or create a “significant increase in paper product problems.”
Regarding the Sheriffs “slippery slope” argument, the evidence does not establish that overturning Butte County’s mail policy would result in a flood of unsolicited mail. The Sheriff presented no evidence that other publishers are likely to request distribution in the jail. In fact, Lt. Flicker testified that he was only aware of three instances in twenty-six years in which someone had asked to distribute unsolicited mail. Butte County’s ban on unsolicited commercial mail was not put in writing until 2004. Thus, the -virtual absence of requests to distribute such mail more likely reflects a lack of interest in reaching the jail’s population than a reaction to the jail’s mail policy. We do “not accord defendants deference on the basis of mere speculation,” and that is all the Sheriff has offered on this point. See Cal. First Amendment Coal., 299 F.3d at 884.
However, the Sheriff has established that distributing the magazine itself would have a significant impact on the allocation of jail resources. CJ&A wants to introduce almost 2,000 pages of unsolicited paper into the jail every week, even as jail officials work to reduce the quantity of paper available to inmates. The Sheriffs evidence supports an inference that if thousands of pages of unsolicited paper are distributed in the jail every month, unsupervised inmates will use at least some of those pages for “nefarious acts,” which will force a jail staff that is already stretched thin to respond to and remedy those violations.
In this situation, the court must be “particularly deferential to the informed discretion of corrections officials.” Turner, 482 U.S. at 90, 107 S.Ct. 2254; see also O’Lone v. Estate of Shabazz, 482 U.S. 342, 353, 107 S.Ct. 2400, 96 L.Ed.2d 282 (1987) (“We take this opportunity to reaffirm our refusal, even where claims are made under the First Amendment, to substitute our judgment on ... difficult and sensitive matters of institutional administration, for the determinations of those charged with the formidable task of running a prison.”) (internal citation and quotation marks omitted). Therefore, the third Turner factor favors the' Sheriff.
D
The fourth and final Turner factor asks “whether the existence of easy and obvious alternatives indicates that the regulation is an exaggerated response by prison officials.” Hrdlicka, 631 F.3d at 1054 (quoting PLN II, 397 F.3d at 699). However, “[t]his is not a ‘least restrictive alternative’ test: prison officials do not have to set up and then shoot down every conceivable alternative method of accommodating the claimant’s constitutional complaint.” Turner, 482 U.S. at 90-91, 107 S.Ct. 2254.
CJ&A argues that - because its magazine is widely distributed at other jails, Butte County’s ban on unsolicited commercial mail must be an “exaggerated response” to. the problems posed by paper in the jail. It is true that “the policies followed at other well-run institutions [are] relevant to a determination of the need for a particular type of restriction.” Morrison, 261 F.3d at 905 (quoting Martinez, 416 U.S. at 414 n.14, 94 S.Ct. 1800, rev’d on other grounds, Thornburgh, 490 U.S. at 413, 109 S.Ct. 1874). However, not all jails are the same, and the district court found that Butte County uses supervision models that provide far less direct supervision than models employed in some other counties, such as Los. Angeles County.
Therefore, distribution of unsolicited paper may cause more problems in the Butte County Jail than in other jails.
The jail’s installation ,of electronic kiosks also indicates that the mail policy is not an exaggerated response. Lt. Flicker testified that the kiosks were installed to “eliminate as much paper as [possible] in the housing units,” because inmates, commit so many rule violations with paper. The kiosks are not just designed for reading material; jail officials are trying to eliminate from housing units hard copies of .inmate request forms, property release forms, sick slips, grievance forms, and the jail handbook. This confirms that paper has created serious problems at the Butte County Jail, and the jail’s mail policy is not an exaggerated response to those problems.
Because each of the Turner factors favors the Sheriff, we agree with the district court’s determination and hold that Butte County’s ban on inmates’ receipt of unsolicited commercial mail is reasonably related to a legitimate penological objective and therefore does not violate the First Amendment,
IV
Captions in the final pages of its opening brief indicate that CJ&A appeals the district court’s post-trial admission of the Jones declaration, and its denial of CJ&A’s motion for relief from judgment and motion to re-open discovery. But “[a] caption is not an argument.” Affordable Housing Dev. Corp. v. City of Fresno, 433 F.3d 1182, 1192 (9th Cir. 2006). An appellant’s brief must contain the “appellant’s contentions and the reasons for them, with citations to the authorities and parts of the record on which the appellant relies.” Fed. R. App. P. 28(a)(8)(A). “Issues raised in a brief which are not supported by argument are deemed abandoned.” Leer v. Murphy, 844 F.2d 628, 634 (9th Cir. 1988).
CJ&A does not explain anywhere in its opening or reply brief why it objected to the admission of the Jones declaration or why it was an abuse of discretion 'for the district court to accept it.
As for the denial of relief from judgment and motion to re-open discovery, CJ&A’s opening brief does little more than state the standard of review and the relevant Rules of Civil Procedure. It references “newly discovered, evidence concerning kiosks,” but it does not explain what new evidence it could have uncovered about the kiosks, or why it was error for the district court to deny its motion. Its reply brief does not clarify the matter,.
Therefore, we hold that CJ&A has abandoned its arguments' related to the post-trial admission of the Jones declaration and its appeal of the. district court’s denial of its motion for relief from judgment and motion to re-open discovery.
Costs are awarded to the Appellee.
The district court’s judgment following trial on the merits is AFFIRMED.