GRIFFITH, Circuit Judge:

Guantanamo Bay detainees challenge two new policies they claim place an undue burden on their ability to meet with their lawyers. The district court upheld the detainees' challenge, but we reverse, concluding that the new policies are reasonable security precautions.

I

The first challenged policy concerns where the detainees may meet with their lawyers. In the past, detainees at Guantanamo Bay would meet with visitors in nearby Camp Echo, to which they were driven in vans, or occasionally in Camps 5 and 6, the camps where most detainees are housed. Meetings in the housing camps would take place in small interview rooms with a guard posted outside the door. It is easier to monitor detainees' meetings with visitors in Camp Echo. There is no need to post a guard outside each meeting because the interview rooms are equipped with video-monitoring equipment, and visitors can summon a guard at the touch of a button. The Camp Echo rooms are also larger than those in the housing camps and include restroom facilities and space for prayer, which means that guards need not move detainees to other rooms mid-meeting to use the bathroom or worship, as they must in the housing camps. Citing the ability to provide more security with fewer guards at Camp Echo, in September 2012 the government implemented a new policy that required that all detainee meetings with visitors take place there instead of in the housing camps.

The second challenged policy involves the search the detainees must undergo when meeting with their lawyers. It has long been Guantanamo policy that detainees are searched both before and after any meeting with a visitor. Standard protocol in military prisons calls for a non-invasive search of the genital area of a prisoner. In the past, searches at Guantanamo departed from that element of the protocol in an effort to accommodate the religious sensibilities of the detainees. Under the old policy, guards would grasp a detainee's waistband and shake his pants in an attempt to dislodge any items that might be hidden, careful to avoid contact with a detainee's genital area. Concerns arose that not searching the genital area was posing a security threat. Those concerns escalated with the suicide of a detainee who took an overdose of medication that he had smuggled into his cell and the discovery of shanks, a wrench, and other weapons in the housing camps that had evaded the searches.

In May 2013 the government revised the search procedures for Guantanamo to conform to standard military prison procedure. According to the protocol, the guard places his hand as a "wedge between the scrotum and thigh, and us[es] the flat hand to press against the groin to detect anything foreign attached to the body. A flat hand is used to ensure no contraband is hidden between the buttocks." The guard also passes a hand-held metal detector a few inches over the detainee's body, including the area of his groin and buttocks. At no time is the detainee's groin visually exposed to the guard.

Detainees challenged these two new policies in habeas corpus proceedings in district court, arguing that they have the purpose and effect of discouraging meetings with their counsel. The detainees claimed that their poor health made it difficult to make the trip by van to meet with their lawyers in Camp Echo and that their religious beliefs made it impossible to meet with counsel at all if genital searches were required to do so. The detainees sought an order permitting them to meet with counsel within the housing camps and without being subject to the new search procedures.

The district court granted the detainees' motion in part. The district court found that the new procedures were an exaggerated response to overstated security concerns, concluding that the rationales offered by the government were but a pretext for the real purpose, which was to restrict detainees' access to counsel. The court entered an order barring use of the new search procedures when meeting with counsel. It also ordered that ill and injured detainees be allowed to meet with their lawyers in the housing camps instead of in Camp Echo. See In re Guantanamo Bay Detainee Litig., 953 F.Supp.2d 40, 59-61 (D.D.C.2013). The government appealed, and we stayed the district court's order pending resolution of this appeal.

II

There is no doubt that we have jurisdiction over an appeal from a district court order granting injunctive relief, 28 U.S.C. § 1292(a)(1); see also Salazar ex rel. Salazar v. District of Columbia, 671 F.3d 1258, 1261-62 (D.C.Cir.2012), but there is a question in this case whether the district court had jurisdiction to issue that order in the first place. Congress has granted district courts jurisdiction to hear habeas claims. 28 U.S.C. § 2241(a); see also Rasul v. Bush, 542 U.S. 466, 481, 124 S.Ct. 2686, 159 L.Ed.2d 548 (2004) (holding that § 2241 extends to Guantanamo detainees). But in the Military Commissions Act of 2006(MCA), Congress barred the federal courts from hearing the habeas claims of Guantanamo detainees. 28 U.S.C. § 2241(e)(1). The MCA also stripped the federal courts of jurisdiction over "any other action ... relating to any aspect of [their] detention, transfer, treatment, trial, or conditions of confinement." Id. § 2241(e)(2).

In Boumediene v. Bush, the Supreme Court invalidated subsection (e)(1)'s ban on habeas claims of Guantanamo detainees, 553 U.S. 723, 792, 128 S.Ct. 2229, 171 L.Ed.2d 41 (2008), but (e)(2) remains a bar to any "other action" by detainees, see Al-Zahrani v. Rodriguez, 669 F.3d 315, 319 (D.C.Cir.2012). Thus, the district court has jurisdiction under § 2241(a) to hear the detainees' habeas challenges, but is prohibited by (e)(2) from hearing any of their other claims. The government contends that the detainees' claims in this matter do not sound in habeas and are therefore barred by (e)(2) because they relate to their "treatment" and "conditions of confinement." The district court found jurisdiction, holding that the alleged interference with access to counsel infringed the right to habeas relief announced in Boumediene. See In re Guantanamo Bay Detainee Litig., 953 F.Supp.2d at 49-50.

We need not determine whether the district court's view of the scope of habeas is correct, for this challenge falls squarely within the jurisdiction we recognized recently in Aamer v. Obama, 742 F.3d 1023 (D.C.Cir.2014). In Aamer, we held that challenges to conditions of confinement can properly "be raised in a federal habeas petition under section 2241," and when so raised are not barred by (e)(2)'s prohibition on non-habeas actions. Id. at 1030, 1038. The government has expressly conceded that the procedures challenged by these habeas petitions are "conditions of confinement." Br. of Appellant at 17-19. The district court thus had jurisdiction under Aamer, and we need not address other jurisdictional theories.

III

We review constitutional challenges to prison policies under the test announced by the Supreme Court in Turner v. Safley, 482 U.S. 78, 89, 107 S.Ct. 2254, 96 L.Ed.2d 64 (1987). This deferential standard applies to military detainees as well as prisoners. See Florence v. Bd. of Chosen Freeholders of Cnty. of Burlington, ___ U.S. ___, 132 S.Ct. 1510, 1518, 182 L.Ed.2d 566 (2012) (applying the Turner test in the context of pre-trial detention); United States v. White, 2014 WL 354661 (N.M.Ct.Crim.App. Jan. 31, 2014) (applying the Turner test to challenges to policies in a military prison); United States v. Phillips, 38 M.J. 641, 642-43 (A.C.M.R. 1993) aff'd, 42 M.J. 346 (C.A.A.F.1995) (same); see also Amatel v. Reno, 156 F.3d 192, 196 (D.C.Cir.1998) (observing that in the military context, the "government is permitted to balance constitutional rights against institutional efficiency" in a manner similar to the Turner test).

In Turner, the Supreme Court explained that although incarcerated individuals do not completely lose their constitutional rights, "problems of prison administration" allow the government to restrict those rights in ways that would be unacceptable for persons not incarcerated. To prevent judicial overreaching into matters of prison administration, courts are to uphold prison regulations that "impinge on inmates' constitutional rights" as long as those regulations are "reasonably related to legitimate penological interests," id. at 84-85, 89, 107 S.Ct. 2254 — a stark departure from the "inflexible strict scrutiny" analysis that normally applies when the government infringes on constitutional rights, id. at 89, 107 S.Ct. 2254.

Here, however, the district court took the view that Turner's deference to reasonable prison regulations does not apply to habeas claims, holding that "[s]ince the right to seek habeas relief is not limited or withdrawn in the prison context, neither may the Executive or the Legislature circumscribe the petitioners' right." In re Guantanamo Bay Detainee Litig., 953 F.Supp.2d at 53. Although there is some intuitive appeal to this novel reasoning, we are compelled to reject it because it directly contravenes Lewis v. Casey, 518 U.S. 343, 116 S.Ct. 2174, 135 L.Ed.2d 606 (1996). Lewis involved a class action alleging that inadequacies in the Arizona prison system deprived inmates of their constitutional right to access the courts by limiting the prisoners' ability to bring various types of lawsuits, including habeas petitions. See id. at 346, 354-55, 116 S.Ct. 2174. The Supreme Court held that "Turner's principle of deference" applies to prison officials' interference with inmates' attempts to bring their habeas claims, id. at 350, 361, 116 S.Ct. 2174, foreclosing the district court's suggestion that Turner does not govern a prisoner's claim that his habeas rights have been abridged by prison officials. See also Phillips v. Bureau of Prisons, 591 F.2d 966, 974 (D.C.Cir.1979) (applying a Turner-like test to prison regulations limiting access to paralegals); cf. Toolasprashad v. Bureau of Prisons, 286 F.3d 576, 584-85 (D.C.Cir.2002) (applying Turner to allow limitations on prisoners' ability to file grievances against prison administrators). We therefore proceed to consider the detainees' claims under the Turner framework.1

IV

We assume, without deciding, that the district court was correct in concluding that the detainees' right to habeas includes the right to representation by counsel and that that right has been burdened by the policies that the detainees challenge.2 See Overton v. Bazzetta, 539 U.S. 126, 131-32, 123 S.Ct. 2162, 156 L.Ed.2d 162 (2003) (declining to define the asserted right where, even if such a right existed and was violated, the regulations survived Turner). Turner requires that we look to four factors to determine if these new policies are reasonable: (1) whether there is a "valid, rational connection between the prison regulation and the legitimate governmental interest put forward to justify it," Turner, 482 U.S. at 89, 107 S.Ct. 2254 (internal quotation marks omitted); (2) "whether there are alternative means of exercising the right that remain open to prison inmates," id. at 90, 107 S.Ct. 2254; (3) "the impact accommodation of the asserted constitutional right will have on guards and other inmates, and on the allocation of prison resources generally," id.; and (4) "the absence of ready alternatives" to the regulation, id. Although we examine each factor, the first is the most important. Amatel, 156 F.3d at 196 ("[T]he first factor looms especially large. Its rationality inquiry tends to encompass the remaining factors...."); see also Beard v. Banks, 548 U.S. 521, 532, 126 S.Ct. 2572, 165 L.Ed.2d 697 (2006) (plurality opinion).

Prison security, the government's asserted purpose for the challenged policies, is beyond cavil a legitimate governmental interest. See Bell v. Wolfish, 441 U.S. 520, 546-47, 99 S.Ct. 1861, 60 L.Ed.2d 447 (1979). Turner teaches that, and common sense shouts it out. The only question for us is whether the new policies are rationally related to security. We have no trouble concluding that they are, in no small part because that is the government's view of the matter. "The task of determining whether a policy is reasonably related to legitimate security interests is peculiarly within the province and professional expertise of corrections officials." Florence, 132 S.Ct. at 1517 (internal quotation marks omitted). We must accord "[p]rison administrators ... wide-ranging deference in the adoption and execution of policies and practices that in their judgment are needed to preserve internal order and discipline and to maintain institutional security." Bell, 441 U.S. at 547, 99 S.Ct. 1861 (emphasis added); see Florence, 132 S.Ct. at 1517; cf. Phillips, 591 F.2d at 972.

The touchstone of our deference, of course, is whether the government's assertion of a connection between prison security and the challenged policy is reasonable. Here, Guantanamo officials explained that they adopted the new search policies to address the risk to security posed by hoarded medication and smuggled weapons. It stands to reason that enhancing the thoroughness of searches at Guantanamo in the way called for by standard Army prison protocol would enhance the effectiveness of the searches. See Florence, 132 S.Ct. at 1516-17. The detainees make no claim to the contrary. Instead, they argue that more thorough searches are not needed during their visits with counsel because the government failed to provide evidence that the contraband was smuggled into the housing camps during these visits. But the authorities at Guantanamo do not know how or when detainees obtain contraband. Cf. Shaw v. Murphy, 532 U.S. 223, 231, 121 S.Ct. 1475, 149 L.Ed.2d 420 (2001) ("Prisoners have used legal correspondence as a means for passing contraband."); Wolff v. McDonnell, 418 U.S. 539, 577, 94 S.Ct. 2963, 41 L.Ed.2d 935 (1974) ("The possibility that contraband will be enclosed in letters, even those from apparent attorneys, surely warrants prison officials' opening the letters."). In light of such uncertainty and the fact that smuggling takes place, we think administering a more thorough search in connection with attorney visits as well as with any other detainee movements or meetings is a reasonable response to a serious threat to security at Guantanamo.

Likewise, it is reasonable to require that all meetings between detainees and their visitors, including counsel, take place in Camp Echo, which requires fewer guards than the housing camps. Each meeting room in Camp Echo, unlike those in the detainees' housing camps, has a restroom and a space for prayer, which means that guards are not needed to transfer detainees mid-meeting. And the video monitoring in Camp Echo eliminates the need to post guards outside each meeting room, as is necessary in Camps 5 and 6. Guards who would have to stand sentry if the visits took place in a housing camp are instead available for postings elsewhere at Guantanamo, enhancing the facility's overall security.

The district court failed to defer to the government's justifications for the new policies, concluding that they were not rationally related to a legitimate government interest. The court required proof from the military that the old procedures were ineffective and in need of change and that the detainee who committed suicide had managed to repeatedly evade the search by hiding the hoarded medication in his groin area. The district court also dismissed the military's expert judgment that some of the guards needed for monitoring visits with detainees in their housing camps could be better used for other security needs, substituting its own assessment that "allowing attorney-client meetings [in the housing camps] would divert a maximum of two to three guards in Camp 5 and four to six guards in Camp 6. The Court is confident the [military] can spare these guards...." In re Guantanamo Bay Detainee Litig., 953 F.Supp.2d at 61.

This misapprehends something fundamental about challenges to prison administration: "The burden ... is not on the State to prove the validity of prison regulations but on the prisoner to disprove it." Overton, 539 U.S. at 132, 123 S.Ct. 2162; see also O'Lone v. Estate of Shabazz, 482 U.S. 342, 350, 107 S.Ct. 2400, 96 L.Ed.2d 282 (1987) ("By placing the burden on prison officials to disprove the availability of alternatives, the approach articulated by the Court of Appeals fails to reflect the respect and deference that the United States Constitution allows for the judgment of prison administrators."). The district court required no such showing of the detainees and erred by failing to defer to the reasonable explanation of Guantanamo officials for decisions within their area of authority and expertise.

Turner next requires that we consider whether the new policies leave the detainees with some other means to exercise their right to counsel. Detainees who forgo visits with their lawyers to avoid the searches can still communicate with counsel via letter. Supreme Court precedent teaches that alternative means of exercising the claimed right "need not be ideal, however; they need only be available." See Overton, 539 U.S. at 135, 123 S.Ct. 2162. But we need not decide whether letters are an adequate replacement for meetings in person, because even if we were to agree with the detainees that they are not, the lack of an alternative "is not conclusive of the reasonableness of the [regulation]" because the other factors must still be considered, Beard, 548 U.S. at 532, 126 S.Ct. 2572 (plurality opinion) (internal quotation marks omitted).

Both of the remaining factors cover much of the same ground as the first and reinforce our conclusion that these policies are reasonable. See Amatel, 156 F.3d at 196. As to the third factor, the impact of an accommodation, we have already concluded that the new search procedures promote the safety of the guards and inmates by more effectively preventing the hoarding of medication and the smuggling of dangerous contraband, and thus the accommodation the detainees seek would necessarily have a negative impact "on guards and other inmates." See Turner, 482 U.S. at 90, 107 S.Ct. 2254; Beard, 548 U.S. at 532, 126 S.Ct. 2572 (plurality opinion). Allowing counsel meetings with detainees to take place in the housing camps instead of Camp Echo would burden "the allocation of prison resources." See Turner, 482 U.S. at 90, 107 S.Ct. 2254.

Finally, the detainees have pointed to no "ready alternative[]" to the new policies. Id. To be "ready," a policy must be an "obvious regulatory alternative that fully accommodates the asserted right while not imposing more than a de minimis cost to the valid penological goal." Overton, 539 U.S. at 136, 123 S.Ct. 2162. The detainees' suggested alternative of reverting to the old policies does not meet this "high standard." Id. Having already determined that we defer to the military's judgment that the old policies hinder the government's interest in security, we can hardly say that they are nonetheless "ready alternatives." In the considered and experienced judgment of Guantanamo administrators, the old policies contributed to the troubling lapses in security. We will not second-guess that determination. See id.; see also Thornburgh v. Abbott, 490 U.S. 401, 419, 109 S.Ct. 1874, 104 L.Ed.2d 459 (1989) ("[W]hen prison officials are able to demonstrate that they have rejected a less restrictive alternative because of reasonably founded fears that it will lead to greater harm, they succeed in demonstrating that the alternative they in fact selected was not an `exaggerated response' under Turner.").

The district court's very different take on these reasonable changes to policy at Guantanamo appears to stem from its view that the changes in policy were pretextual and the result of the government's plan to inhibit detainees' access to counsel. It is unclear what role, if any, motive plays in the Turner inquiry. Compare Hammer v. Ashcroft, 570 F.3d 798, 803 (7th Cir.2009) (en banc), with Salahuddin v. Goord, 467 F.3d 263, 276-77 (2d Cir.2006), and Quinn v. Nix, 983 F.2d 115, 118 (8th Cir.1993). Even if some quantum of evidence of an unlawful motive can invalidate a policy that would otherwise survive the Turner test, the evidence of unlawful motive in this case is too insubstantial to do so. The district court drew inferences from past conduct by former commanders and dismissed as unbelievable the sworn statements of military officials. We find such an approach unwarranted. Although we must not give prison administrators a free hand to disregard fundamental rights, this case is a far cry from instances where administrators have acknowledged their intent to extinguish prisoner rights and acted accordingly. Cf. Hammer, 570 F.3d at 802-03. The tenuous evidence of an improper motive to obstruct access to counsel in this case cannot overcome the legitimate, rational connection between the security needs of Guantanamo Bay and thorough searches of detainees.

V

For the foregoing reasons, the decision of the district court is reversed.