The United States is pressing hard to get hold of National Security Agency leaker Edward Snowden. But if and when Snowden is apprehended, what then? This question deserves attention, too, because the denouement to this drama may be unpleasant not just for Snowden, but for his captors as well.

The downside for Snowden is straightforward. He faces prison time in this country. Even if his disclosures were well-intentioned or exposed any misconduct, no court has allowed a classified information leaker to escape liability on those grounds.

In the past, leakers typically got off easy. The vast majority were never charged with any crime. The first media leaker convicted under the Espionage Act, Samuel Morison, received a two-year sentence, served eight months, and was later pardoned. However, the Obama administration has taken leak enforcement to a new level. And Snowden’s security breach was so remarkable that his sentence could be much stiffer.

If the case law is on its side, why would the government have reason to worry about prosecuting Snowden?

One source of concern is the jury. Snowden says his leaks revealed an unconstitutional and undemocratic system of surveillance. Polls suggest that many Americans agree. Even if the judge instructs the jury to set aside its views on the rightness or wrongness of Snowden’s acts, there is no guarantee it will. Jurors might be tempted to acquit Snowden, not because they believe he is factually innocent but because they believe he was morally justified.

It has happened before—in England. In 1985, Clive Ponting looked destined for prison after leaking Ministry of Defence documents that called into question the official story of the Falklands War. Ponting fessed up to being the source. The jury voted to acquit him nevertheless, and in so doing helped catalyze a movement to liberalize the laws against unauthorized disclosures.

Additional concerns relate to the trial. Snowden would no doubt obtain high-powered lawyers. Protesters would ring the courthouse. Journalists would camp out inside. As proceedings dragged on for months, the spotlight would remain on the N.S.A.’s spying and the administration’s pursuit of leakers. Instead of fading into obscurity, the Snowden affair would continue to grab headlines, and thus to undermine the White House’s ability to shape political discourse.

A trial could turn out to be much more than a distraction: It could be a focal point for domestic and international outrage. From the executive branch’s institutional perspective, the greatest danger posed by the Snowden case is not to any particular program. It is to the credibility of the secrecy system, and at one remove the ideal of our government as a force for good.

To do their jobs, the U.S. intelligence agencies must be able to keep secrets. But even more fundamentally, they must be able to sustain a democratic mandate. They need Congress to give them the money and the discretion to engage in clandestine activities. They need the Foreign Intelligence Surveillance Court to approve their domestic eavesdropping. They need technology companies and allied governments to cooperate with them. They need voters to elect presidents and legislators who support their mission. They need talented young people to want to sign up.

Snowden’s leaks have at least provisionally compromised public trust in these agencies, as well as programs like PRISM and Boundless Informant. (Pause to savor that label—Boundless Informant. The very title of the program condemns it.) A criminal case against Snowden risks deepening and entrenching this alienation. The case would invite even more scrutiny, and potentially unprecedented judicial scrutiny, of the N.S.A.’s practices. It would feed the perception that this administration is determined to stifle dissent. Above all, in the figure of Snowden, it would give skeptics worldwide a concrete symbol around which to rally.

Because it is so secretive, the N.S.A. must tend carefully to its legitimacy. Conspiracy theories and Big Brother fears always swirl at the margins of respectable opinion, threatening to go mainstream. A rogue leaker is a serious problem for the agency’s short-term intelligence operations. A rogue leaker who comes to be seen by a large number of Americans as a persecuted truth-teller is a serious problem for its long-term political viability.

More broadly, Snowden’s case may clash with certain foreign policy goals. The United States often wants other countries’ dissidents to be able to find refuge abroad; this is a longstanding plank of its human rights agenda. The United States also wants illiberal regimes to tolerate online expression that challenges their authority; this is the core of its developing Internet freedom agenda.

Snowden’s prosecution may limit our soft power to lead and persuade in these areas. Of course, U.S. officials could emphasize that Snowden is different, that he’s not a courageous activist but a reckless criminal. But that is what the repressive governments say about their prisoners, too.

These concerns might seem abstract in comparison to the vividness of Snowden’s transgressions and the concreteness of his revelations, the quiddity of those four laptops and the PowerPoint slides. And so they are. That does not make them any less significant.

Against these costs, the benefits from prosecuting Snowden are no less speculative. If allowing Snowden to remain abroad enhanced his ability to spill secrets, there would be an obvious reason for the U.S. government to want to nab him as quickly as possible. It seems increasingly clear, however, that the government has no chance of securing Snowden’s stash. In addition to the Guardian and the Washington Post, WikiLeaks reportedly was given the files. The Chinese and Russian intelligence services may have acquired them. Unknown others may have still more copies.

The documents Snowden took with him, in short, are never coming back. They are a sunk cost for the government. Prosecuting Snowden can’t reduce that cost and, by inflaming his associates, might even accelerate the process of full public disclosure.

Yet if incapacitating Snowden won’t do any direct good for national security, what about setting an example for potential future leakers? Wouldn’t some of them be scared off by seeing Snowden behind bars? Maybe, but that is not the right deterrence question to ask. The relevant question now is, what is the marginal deterrence value of prosecuting Snowden over and above offering him a plea deal (with a low enough sentence to entice him back) or hounding him into effective exile in a country like Venezuela (which has offered him asylum)?

Not much, possibly. A long prison term is a terrible fate. But even a short prison term would scare any rational person, and exile is a profound punishment as well. Indeed, it is an ancient response to offenses that are viewed as betraying one’s community.

The United States has invested a lot of time, effort, and political capital into trying to apprehend Snowden. Those efforts have gone a long way toward limiting his options. The more the U.S. government continues to insist that nothing short of immediate extradition is acceptable, the more it invites the perception that its diplomacy was a failure rather than a success.

A plea deal or an asylum arrangement would frustrate almost everyone. It wouldn’t satisfy those who are appalled by Snowden’s actions and wish to see a spectacular challenge to U.S. rules and institutions met with the full force of the criminal justice system. It would equally disappoint those who think Snowden deserves a hero’s welcome home.

We are long past the time for ideal solutions, however. If the U.S. government can’t win in this matter, maybe it ought to think about cutting its losses.