Washington ? A sad irony of Barack Obama’s presidency is that a man who wanted to repair U.S. relations abroad has instead had to cope with damaging new strains with allies, following Edward Snowden’s revelations about National Security Agency surveillance overseas.

For the White House, the NSA disclosures have been a bottomless pit. Officials don’t know how much information Snowden took from classified files, or how much he may have stashed in encrypted “cloud” storage. They can inventory the documents he viewed, but they don’t necessarily know if he downloaded and kept them. It’s hard to get in front of a scandal when you don’t know what’s coming next.

As Obama thinks about ways to limit damage and restore confidence among U.S. allies overseas, he’s said to be considering some intriguing possibilities — including privacy protections for foreigners. 

One idea is to apply to foreign surveillance some of the “minimization” procedures the NSA uses, in theory, to shield the identities of “U.S. persons” whose “metadata” has been collected but aren’t targets of any terrorism or criminal probe. If the U.S. made credible minimization pledges to foreigners, the content of their personal messages couldn’t legally be accessed, even if the call records themselves were obtained.

Just considering this question is unsettling to U.S. intelligence officials, who for years have responded to queries about privacy issues with a bland dismissal. “The Fourth Amendment doesn’t apply to foreigners,” officials will say. The dirty little secret (not so secret anymore) is that the job of spy agencies is to violate other countries’ borders and laws to collect information.

The U.S. nominally supports international privacy rights, in such documents as the 1948 Universal Declaration of Human Rights. But, like most nations, it does so with crossed fingers. One way for the Obama administration to draw a line under the NSA scandal would be to embrace a new international initiative to take privacy rights more seriously. The Fourth Amendment promises that “the right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated.” How might the spirit of that promise be extended to citizens of other countries?

Once you start thinking about legal limits on U.S. foreign snooping, complicated questions arise. Would such limits apply to all foreigners, or just to certain countries? Would they apply only to democratic countries that offer human-rights protections to their own citizens? Would they apply to allies, as a reward? Would the U.S. insist on reciprocal guarantees? And how would any such pledges be credible, given that intelligence is all about doing in a deniable way what you pretend you’re not doing?

“Are there to be two classes of people in society — those who ‘deserve’ rights, and have them, and those who do not?” asks my friend Garrett Epps, a professor of constitutional law at the University of Baltimore, in discussing the Fourth Amendment in his new book, “American Epic,” which examines line by line what the Constitution actually says. His question of who’s entitled to privacy protection is at the heart of the NSA conundrum.

A less complicated post-Snowden reform under White House consideration is to apply a much more rigorous cost-benefit analysis to intelligence gathering in friendly countries. What information does the U.S. really need to know from, say, Germany and France, and what’s superfluous? Did the U.S. obtain any insights from bugging German Chancellor Angela Merkel’s cellphone that remotely justified the political risk? The answer is surely no, but the NSA was on autopilot when the collection began. Not anymore.

A final puzzle is whether to increase the sharing of NSA surveillance information with peeved allies such as France and Germany. That may sound puzzling, given all the indignant complaining from those nations. But their top officials know how valuable NSA information is, and they want more of whatever is legally collected, even if they don’t say so publicly. Indeed, an undercurrent of the NSA scandals is resentment by friendly European and Asian nations at America’s special intelligence sharing with Britain and other English-speaking countries — known collectively as the “Five Eyes,” or, to the French, “les anglo-saxons.”

A complicating factor is that the U.S., perhaps paradoxically given the Snowden disclosures, is more open in its public oversight and discussion of intelligence than almost any other country. In many European nations, intelligence secrets are still, for the most part, not discussed openly. That imbalance makes the post-Snowden dialogue difficult — a study in foreign hypocrisy as well as American excess.