Albert Johnson brought this suit under 42 U.S.C. § 1983. According to his complaint, which the district court dismissed for failure to state a claim on which relief may be granted, female guards at the Cook County Jail are assigned to monitor male prisoners’ movements and can see men naked in their cells, the shower, and the toilet. Johnson sought damages from persons including the President of the Cook County Board and the Chairman of the County’s Buildings and Zoning Commission. Most of the defendants have no relation to the events of which Johnson complains and were properly dismissed because § 1983 does not establish vicarious liability. See Houston v. Sheahan, 62 F.3d 902 (7th Cir.1995). The district court also properly rejected Johnson’s argument that different monitoring patterns in different cellbloeks within the Jail violate the equal protection clause of the fourteenth amendment. 1993 U.S.Dist. Lexis 13681 (N.D.Ill.). Johnson has abandoned on appeal any contention that monitoring in the local courthouse lockup’s bathroom violates the Constitution. But his argument that cross-sex monitoring in the Jail violates the due process clause requires additional discussion in light of Canedy v. Boardman, 16 F.3d 183 (7th Cir.1994), which holds that a right of privacy limits the ability of wardens to subject men to body searches by women, or the reverse. Our ease involves visual rather than tactile inspections, and we must decide whether male prisoners are entitled to prevent female guards from watching them while undressed.
Observation is a form of search, and the initial question therefore is whether monitoring is “unreasonable” under the fourth amendment. So the Supreme Court conceived the issue in Bell v. Wolfish, 441 U.S. 520, 99 S.Ct. 1861, 60 L.Ed.2d 447 (1979), where a pretrial detainee argued that routine inspections of his body cavities violated the Constitution. (Johnson also was a pretrial detainee at the time of the events covered in his complaint, but in light of Wolfish he does not argue that detainees have rights exceeding those of prisoners following conviction.) The Court held that these searches are “reasonable” because they are prudent precautions against smuggling drugs and other contraband into prison. 441 U.S. at 558-60, 99 S.Ct. at 1884-85. Prisoners argued that metal detectors plus supervision of inmates’ contacts with outsiders would be superior to body-cavity inspections. The Court replied that prisons need not adopt the best alternatives. 441 U.S. at 559-60 n. 40, 99 S.Ct. at 1884-85 n. 40. Less-restrictive-alternative arguments are too powerful: a prison always can do something, at some cost, to make prisons more habitable, but if courts assess and compare these costs and benefits then judges rather than wardens are the real prison administrators. Wolfish emphasized what is the animating theme of the Court’s prison jurisprudence for the last 20 years: the requirement that judges respect hard choices made by prison administrators. E.g., Sondin v. Conner, — U.S. —, —, 115 S.Ct. 2293, 2299-2300, 132 L.Ed.2d 418 (1995); O’Lone v. Estate of Shabazz, 482 U.S. 342, 349-50, 107 S.Ct. 2400, 2404-05, 96 L.Ed.2d 282 (1987); Jones v. North Carolina Prisoners’ Labor Union, Inc., 433 U.S. 119, *146125, 97 S.Ct. 2532, 2537-38, 53 L.Ed.2d 629 (1977); Wolff v. McDonnell, 418 U.S. 539, 561-63, 94 S.Ct. 2963, 2977-78, 41 L.Ed.2d 935 (1974).
Wolfish assumed without deciding that prisoners retain some right of privacy under the fourth amendment. Five years later the Court held that they do not. Hudson v. Palmer, 468 U.S. 517, 526-30, 104 S.Ct. 3194, 3200-02, 82 L.Ed.2d 393 (1984), observes that privacy is the thing most surely extinguished by a judgment committing someone to prison. Guards take control of where and how prisoners live; they do not retain any right of seclusion or secrecy against their captors, who are entitled to watch and regulate every detail of daily life. After Wolfish and Hudson monitoring of naked prisoners is not only permissible — wardens are entitled to take precautions against drugs and weapons (which can be passed through the alimentary canal or hidden in the rectal cavity and collected from a toilet bowl) — but also sometimes mandatory. Inter-prisoner violence is endemic, so constant vigilance without regard to the state of the prisoners’ dress is essential. Vigilance over showers, vigilance over cells — vigilance everywhere, which means that guards gaze upon naked inmates.
Johnson mentions the fourth amendment but ignores Wolfish and Hudson. His principal argument uses the due process clause; and because he does not seek a hearing, he is invoking principles of substantive due process. Yet courts should not reverse the outcome of a fourth amendment analysis in the name of substantive due process. Graham v. Connor, 490 U.S. 386, 109 S.Ct. 1865, 104 L.Ed.2d 443 (1989), and Albright v. Oliver, — U.S. —, 114 S.Ct. 807, 127 L.Ed.2d 114 (1994), hold that substantive due process is not an appropriate substitute for analysis under provisions of the Constitution that address a subject directly, and in particular does not trump the fourth amendment. “Privacy” has too many other connotations — from the right of reproductive autonomy that has nothing to do with searches and seizures to the common law right to control the publication of certain facts about oneself, including the depiction of one’s naked body, see Haynes v. Alfred A. Knopf, Inc., 8 F.3d 1222, 1229-30 (7th Cir.1993) — to be a useful substitute for the fourth amendment (or, as we discuss below, the eighth).
What is more, moving ground from the fourth amendment to the fifth would not help Johnson. Under the due process clause the question is whether the regulation is “reasonably related to legitimate penological interests.” Turner v. Safley, 482 U.S. 78, 89, 107 S.Ct. 2254, 2261-62, 96 L.Ed.2d 64 (1987). Surveillance of prisoners is essential, as Wolfish establishes. Observation of cells, showers, and toilets is less intrusive than the body-cavity inspections Wolfish held permissible. Guards do the surveillance. Male guards and female guards too — for Title VII of the Civil Rights Act of 1964 opens prisons to women and requires states to hire them unless sex is a bona fide occupational qualification, a high standard of necessity. Dothard v. Rawlinson, 433 U.S. 321, 97 S.Ct. 2720, 53 L.Ed.2d 786 (1977); United States v. Gregory, 818 F.2d 1114 (4th Cir.1987) (rejecting an argument that a desire to curtail cross-sex monitoring of naked prisoners makes sex a bona fide occupation qualification for prison guards); see also United Auto Workers v. Johnson Controls, Inc., 499 U.S. 187, 111 S.Ct. 1196, 113 L.Ed.2d 158 (1991). Unless female guards are shuffled off to back office jobs, itself problematic under Title VII, they are bound to see the male prisoners in states of undress. Frequently. Deliberately. Otherwise they are not doing their jobs. Smith v. Fairman, 678 F.2d 52 (7th Cir.1982), puts two and two together, holding that in light of Title VII female guards are entitled to participate in the normal activities of guarding, including pat-down searches of male inmates. We held in Torres v. Wisconsin Department of Health & Social Services, 859 F.2d 1523 (7th Cir.1988) (en banc), a case filed by guards under Title VII, that a state could exclude men from one of its four prisons, in order to promote the female prisoners’ rehabilitation. Torres did not say that the Constitution requires this exclusion; instead we deferred to the judgment of prison administrators that they needed to limit cross-sex monitoring to achieve penological objectives. Today deference leads to the opposite result: Cook County does not believe that cross-sex monitoring imperils its *147mission, and evenhanded willingness to accept prison administrators’ decisions about debatable issues means that Johnson cannot prevail under the due process clause.
After holding in Hudson that prisoners lack any reasonable expectation of privacy under the fourth amendment, the Court remarked that a prisoner could use the eighth amendment to overcome “calculated harassment unrelated to prison needs.” 468 U.S. at 530, 104 S.Ct. at 3202. Similarly, the Court observed in Graham that the eighth amendment offers some protection supplementary to the fourth. 490 U.S. at 392, 394, 109 S.Ct. at 1869, 1870. We therefore think it best to understand the references to “privacy” in Canedy and similar eases as invocations of the eighth amendment’s ban on cruel and unusual punishments. See Jordan v. Gardner, 986 F.2d 1521 (9th Cir.1993) (en banc), which makes explicit the role of that provision.
Johnson’s complaint (and the brief filed on his behalf in this court by a top-notch law firm) do not allege either particular susceptibility or any design to inflict psychological injury. A prisoner could say that he is especially shy — perhaps required by his religion to remain dressed in the presence of the opposite sex — and that the guards, knowing this, tormented him by assigning women to watch the toilets and showers. So, too, a prisoner has a remedy for deliberate harassment, on account of sex, by guards of either sex. Johnson does not allege this or anything like it. His case therefore does not present the sort of claim that Hudson holds in reserve. It does not satisfy the more general requirements of the eighth amendment either.
One who makes a claim under the cruel and unusual punishments clause must show that the state has created risk or inflicted pain pointlessly. “After incarceration, only the unnecessary and wanton infliction of pain ... constitutes cruel and unusual punishment forbidden by the Eighth Amendment.” Whitley v. Albers, 475 U.S. 312, 319, 106 S.Ct. 1078, 1084, 89 L.Ed.2d 251 (1986) (internal quotations omitted). See also Rhodes v. Chapman, 452 U.S. 337, 101 S.Ct. 2392, 69 L.Ed.2d 59 (1981); Wilson v. Seiter, 501 U.S. 294, 298-300, 111 S.Ct. 2321, 2323-2325, 115 L.Ed.2d 271 (1991); Helling v. McKinney, — U.S. —, 113 S.Ct. 2475, 125 L.Ed.2d 22 (1993). Does cross-sex monitoring serve a function beyond the infliction of pain? Monitoring is vital, but how about the cross-sex part? For this there are two justifications.
First, it makes good use of the staff. It is more expensive for a prison to have a group of guards dedicated to shower and toilet monitoring (equivalently, a group that can do every function except this) than to have guards all of whom can serve each role in the prison. If only men can monitor showers, then female guards are less useful to the prison; if female guards can’t perform this task, the prison must have more guards on hand to cover for them. It is a form of featherbedding. O’Lone held that an interest in the efficient deployment of the staff permits the prison to block inmates from attending religious services, although religion has powerful protection in the first amendment. Similarly, an interest in efficient deployment of the staff supports cross-sex monitoring. See Timm v. Gunter, 917 F.2d 1093, 1102 (8th Cir.1990), which concludes that “opposite-sex surveillance of male inmates, performed on the same basis as same-sex surveillance,” is constitutionally permissible. By the same token, the prison may assign homosexual male guards to monitor male prisoners, heterosexual male guards to monitor effeminate male homosexual prisoners, and so on. There are too many permutations to place guards and prisoners into multiple classes by sex, sexual orientation, and perhaps other criteria, allowing each group to be observed only by the corresponding groups that occasion the least unhappiness.
Second, cross-sex monitoring reduces the need for prisons to make sex a criterion of employment, and therefore reduces the potential for conflict with Title VII and the equal protection clause. Cells and showers are designed so that guards can see in, to prevent violence and other offenses. Prisoners dress, undress, and bathe under watchful eyes. Guards roaming the corridors are bound to see naked prisoners. A prison *148could comply with the rule Johnson proposes, and still maintain surveillance, only by relegating women to the administrative wing, limiting their duties (thereby raising the cost of the guard complement), or eliminating them from the staff.
To the riposte that Title VII and the equal protection clause can’t authorize a violation of the eighth amendment, we rejoin: True enough, but not pertinent. A warden must accommodate conflicting interests — the embarrassment of reticent prisoners, the entitlement of women to equal treatment in the workplace. A state may reject the prisoner’s claim if it has a reason, as Wolfish establishes for a substantially greater intrusion. The interest of women in equal treatment is a solid reason, with more secure footing in American law than prisoners’ modesty, leading to the conclusion that there is no violation of the eighth amendment. We held as much already in Smith v. Fairman. When interests clash, a judge must prefer those based on legislative decisions over those that reflect their own views of sound policy. The premise of judicial review is that the Constitution is an authoritative decision binding on all branches of government; when it has only such substance as judges pour into it themselves, the decisions of the elected branches prevail. Canedy accordingly avowed reluctance to do more than forbid cross-sex body searches, 16 F.3d at 187, which it conceived as pointless debasement. Anonymous visual inspections from afar are considerably less intrusive and carry less potential for “the unnecessary and wanton infliction of pain”. To the extent incautious language in Canedy implies that deliberate visual inspections are indistinguishable from physical palpitations, its discussion is dictum. Further reflection leads us to conclude that it should not be converted to a holding.
How odd it would be to find in the eighth amendment a right not to be seen by the other sex. Physicians and nurses of one sex routinely examine the other. In exotic places such as California people regularly sit in saunas and hot tubs with unclothed strangers. Cf. Miller v. South Bend, 904 F.2d 1081 (7th Cir.1990) (en banc) (holding that there is a constitutional right to dance nude in public), reversed under the name Barnes v. Glen Theatre, Inc., 501 U.S. 560, 111 S.Ct. 2456, 115 L.Ed.2d 504 (1991). Most persons’ aversion to public nudity pales compared with the taboo against detailed inspections of body cavities, yet the Court found no constitutional obstacle to these in Wolfish; the Constitution does not require prison managers to respect the social conventions of free society. Drug testing is common, although this often requires observation of urination. Vernonia School District 47J v. Acton, c U.S. —, 115 S.Ct. 2386, 132 L.Ed.2d 564 (1995) (drug testing of seventh grade boy as condition of participation in sports is “reasonable” under the fourth amendment); see also Dimeo v. Griffin, 943 F.2d 679, 682-83 (7th Cir.1991) (en banc), in which this court treated the imposition on privacy as slight. More to the point, the clash between modesty and equal employment opportunities has been played out in sports. Women reporters routinely enter locker rooms after games. How could an imposition that male athletes tolerate be deemed cruel and unusual punishment?
Some cases say that the Constitution forbids deliberate cross-sex monitoring (as opposed to infrequent or accidental sightings). See Cornwell v. Dahlberg, 963 F.2d 912, 916-17 (6th Cir.1992) (basing this conclusion on the fourth amendment, but without mentioning Hudson); Lee v. Downs, 641 F.2d 1117, 1120 (4th Cir.1981) (decided three years before Hudson). Decisions such as Timm and Grummett v. Rushen, 779 F.2d 491 (9th Cir.1985), which hold that cross-sex monitoring is constitutional, could be treated as fact-bound, although some of their language is unqualified (we have quoted such a passage from Timm). Each emphasized that the female guards’ views were not universally unobstructed. But if this is important (and we do not think it is), Johnson’s own complaint brings the case within the scope of Timm. Johnson alleges that
when a female correctional officer is assigned to work a dorm it is her duty and responsibility to make counts, also to constantly supervise all inmates in the dorms, making periodic, unannounced spot checks of inmates in their living area, and surveying in the remainder of the area such *149as the general toilet, and shower facilities, which is in an open unobstructed area, except by a thin sheet that can be seen through.
Thus Johnson tells us that the Jail offers some, but imperfect, shielding from guards’ observation, exactly the situation that the eighth circuit held permissible in Timm. We agree with that conclusion. See also Jordan v. Gardner, 986 F.2d at 1545-67 (Wallace, Wiggins, Trott & Kleinfeld, JJ., dissenting).
Any practice allowed under the due process analysis of Turner is acceptable under the eighth amendment too — not only because the objective component of cruel and unusual punishment is more tolerant toward wardens, but also because the eighth amendment has a demanding mental-state component. Farmer v. Brennan, — U.S. —, 114 S.Ct. 1970, 128 L.Ed.2d 811 (1994), holds that the standard is criminal recklessness. The guard or warden must want to injure the prisoner or must know of and disregard a substantial risk that harm will befall the prisoner. Johnson does not allege that any of the defendants sought to humiliate him. Although he filed the complaint pro se, his lawyer did not add this allegation to the brief and showed no inclination to advance it when pressed at oral argument. Of course, we must grant Johnson the benefit of all allegations in the complaint and everything he might prove consistent with that document. Conley v. Gibson, 355 U.S. 41, 45-46, 78 S.Ct. 99, 101-02, 2 L.Ed.2d 80 (1957); Bartholet v. Reishauer A.G. (Zurich), 953 F.2d 1073, 1078 (7th Cir.1992). The district court assumed that the cross-sex viewing was inadvertent, an inappropriate step when evaluating a complaint under Rule 12(b)(6). But what Johnson wants to show is not that the defendants adopted their policy to cause injury, but that they ignored his sensibilities. He must believe it sufficient to show that they acted deliberately.
Put the eighth amendment aside for a moment and consider the question whether a “deliberate” decision — that is, a considered choice with knowledge of the consequences— establishes “intent” for purposes of constitutional provisions containing a mental-state ingredient. That question has been before the Supreme Court many times, and the answer is “no.” A good example is Personnel Administrator of Massachusetts v. Feeney, 442 U.S. 256, 99 S.Ct. 2282, 60 L.Ed.2d 870 (1979), apropos because it deals with sex discrimination. Massachusetts decided to give military veterans an absolute, lifetime preference in employment. Approximately 98% of veterans are male, and as a result the bureaucracy is overwhelmingly male. A three-judge district court held the preference unconstitutional. Recognizing that the equal protection clause forbids only disparate treatment, and not disparate impact, see Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976), the district court observed that people are deemed to intend the natural and probable consequences of their acts. Massachusetts adopted the preference deliberately, and it maintained the preference after recognizing that it excluded many qualified women from the civil service. The Supreme Court acknowledged all of this but held that deliberate acts, with knowledge of the consequences, do not establish “intent” in the constitutional sense — for, if they did, then the distinction between disparate treatment and disparate impact would collapse as soon as anyone informed the decisionmaker of the impact. After a canvass of its cases, the Court concluded:
“Discriminatory purpose” ... implies more than intent as volition or intent as awareness of consequences. It implies that the decisionmaker ... selected or reaffirmed a particular course of action at least in part “because of,” not merely “in spite of,” its adverse effects upon an identifiable group.
442 U.S. at 279, 99 S.Ct. at 2296 (citation and footnotes omitted). Since Feeney the distinction between choices made “because” the de-cisionmaker wants to achieve particular consequences, and those “in spite of’ unwelcome effects, has been a staple of constitutional law. See, e.g., Miller v. Johnson, — U.S. —, —, 115 S.Ct. 2475, 2488, 132 L.Ed.2d 762 (1995).
Wardens make many choices that have unpleasant consequences for prisoners, and frequently wardens wish that they could do things differently. Budgetary shortfalls may dictate that prisoners five in cramped condi*150tions, even though wardens know that peno-logical purposes would be better served by additional space. The question whether a deliberate choice to put two prisoners in a cell with only 100 square feet of space satisfied the intent component of the eighth amendment came up in Wilson v. Setter. Prisoners alleged that the dilapidated facility had “overcrowding, excessive noise, insufficient locker storage space, inadequate heating and cooling, improper ventilation, unclean and inadequate restrooms, unsanitary dining facilities and food preparation, and housing [of regular inmates] with mentally and physically ill inmates.” 501 U.S. at 296, 111 S.Ct. at 2322. The warden knew all about this, and official decisions led to the problems— for example, the state spent money on guards’ salaries rather than better food facilities. The Court assumed that conditions at the prison fell below objectively permissible standards but held that the prisoners had not demonstrated the essential mental state.
To put this differently, the question in Wilson was whether the mental-state requirement applies to systemic conditions, which affect all prisoners. The Court answered yes, acknowledging that this could perpetuate some unwelcome conditions:
The United States suggests that a state-of-mind inquiry might allow officials to interpose the defense that, despite good-faith efforts to obtain funding, fiscal constraints beyond their control prevent the elimination of inhumane conditions. Even if that were so, it is hard to understand how it could control the meaning of “cruel and unusual punishment” in the Eighth Amendment. An intent requirement is either implicit in the word “punishment” or is not; it cannot be alternately required and ignored as policy conditions might dictate.
501 U.S. at 301-02, 111 S.Ct. at 2325-26. “If the pain inflicted is not formally meted out as punishment by the statute or sentencing judge, some mental element must be attributed to the inflicting officer before it can qualify.” Id. at 300, 111 S.Ct. at 2325 (emphasis in original). No intent to injure means no “punishment”; and no “punishment,” no violation.
Let us test this with an illustration. Suppose the warden decides to issue guns to the guards, a step that in the absence of an ongoing riot violates contemporary norms because weapons create risks. Prisoners may seize them and shoot the guards or each other; guards may discharge them accidentally, injuring the prisoners. The decision to issue the guns is deliberate, and everyone knows that some injuries will follow. The warden hopes that a reduction in violence within the prison will compensate for the new risk. Can a prisoner obtain an injunction excluding guns from the prison on the ground that the risk exceeds the anticipated benefits? Or suppose the inevitable happens: a guard shoots a prisoner. Has the warden violated the eighth amendment? The answer from Whitley is “no,” because the warden did not want harm to come to the prisoners and adopted the policy in an attempt to reduce violence. The policy was not designed to punish anyone and therefore, under Whitley, Wilson, and Farmer, does not violate the eighth amendment. A warden displays “deliberate indifference” only if he ignores the costs to prisoners, excluding them from the calculus of costs and benefits, or if he allows guns into the prison because he wants prisoners to suffer. An incorrect assessment of recognized costs and benefits is just negligence, which does not violate the fifth amendment (even if “gross,” see Archie v. Racine, 847 F.2d 1211, 1218-20 (7th Cir.1988) (en banc)), and does not violate the eighth amendment either. Cf. Collins v. Harker Heights, 503 U.S. 115, 112 S.Ct. 1061, 117 L.Ed.2d 261 (1992) (public policies that create risks for employees do not violate the Constitution, even if the risks are taken knowingly); Walker v. Rowe, 791 F.2d 507 (7th Cir.1986) (same principle, applied to risks that lead to death of prison guards). Yet this gun policy is deliberate in the same sense as the policy permitting cross-sex monitoring, and injury is as predictable as the existence of embarrassed inmates.
Where does this leave us? The fourth amendment does not protect privacy interests within prisons. Moving to other amendments does not change the outcome. Cross-sex monitoring is not a senseless imposition. *151As a reconciliation of conflicting entitlements and desires, it satisfies the Turner standard. It cannot be called “inhumane” and therefore does not fall below the floor set by the objective component of the eighth amendment. And Johnson does not contend that his captors adopted their monitoring patterns because of, rather than in spite of, the embarrassment it causes some prisoners. He does not submit that the warden ignored his sensibilities; he argues only that they received too little weight in the felicific calculus. Like the district court, therefore, we conclude that the complaint fails to state a claim on which relief may be granted.
Affirmed.