Tuesday was a day for straightening stories—some of which were bent more out of shape than others—and for filling in details about the killing of Osama bin Laden. The Pentagon released a “Narrative of Events,” which notes that “the team methodically cleared the compound moving from room to room in an operation lasting nearly 40 minutes.” But the narrative itself is more economical than methodical—as well as a bit different than the account we’d had before. It’s worth reading in full; Jay Carney, the press secretary, read some of it at his briefing, at which he also said that our government was concerned that releasing photographs of bin Laden’s body might be “inflammatory.” (See Philip Gourevitch’s discussion of that point.) Here are some excerpts of the narrative:

In addition to the bin Laden family, two other families resided in the compound: one family on the first floor of the bin Laden building and one family in a second building. One team began the operation on the first floor of the bin Laden house and worked their way to the third floor; a second team cleared the separate building. On the first floor of bin Laden’s building, two Al Qaeda couriers were killed along with a woman who was killed in cross-fire. Bin Laden and his family were found on the second and third floor of the building. There was concern that bin Laden would oppose the capture operation and indeed he resisted. In the room with bin Laden, a women—bin Laden’s wife—rushed the U.S. assaulter and was shot in the leg but not killed. Bin Laden was then shot and killed. He was not armed.

Reading that, it sounds as though the woman who was killed was not bin Laden’s wife, or even on the same floor of the house as he was, and thus not being used by him, as the White House first said, as a “human shield”—certainly not in the sense most of us understood—and that bin Laden’s wife, who “rushed the U.S. assaulter,” survived. (Where is she now?) Bin Laden not being armed is relevant less in a legalistic sense—as Carney said, “resistance does not require a firearm”—than because it suggests a missed, or rather ignored, opportunity. How hard would it have been to arrest him, and to put a man who murdered people in this city on trial in this city?

There are other details: “The body was placed in a weighted bag; a military officer read prepared religious remarks, which were translated into Arabic by a native speaker.”

And there were other storytellers: the BBC quoted an I.S.I. official, but doesn’t say whether he managed to keep a straight face while telling them this:

“the compound was not on our radar, it is an embarrassment for the I.S.I.…. We’re good, but we’re not God.”

That compound was a few hundred yards from a military academy, so “not on our radar” might be the wrong metaphor (as might “not God”). More interestingly, the I.S.I. official told the BBC that several children were in the compound, and that one of bin Laden’s daughters was with him when he was shot; one would like more details about that. (CNN reported, meanwhile, that the White House had three sets of photos: the body, the burial at sea, and the raid, including one of bin Laden’s dead son, who appeared to be about eighteen.)

How much does it matter for us to get all the details right? Isn’t there a larger truth: that bin Laden was a bad man, and a murderer, and a plotter of more murderers, and we got him—imperfectly, maybe, but doing our best? It still matters, a great deal. Our victory over him, ultimately, will depend on whether people in the world feel that we are asking them to live with the indignity of being lied to—or are complicit in the lies we tell ourselves—or are, instead, dealing with them honestly. The soldiers who went after him risked their lives; we can live with the truth, whatever it is.

Read David Remnick, Steve Coll, Lawrence Wright, Jon Lee Anderson, Dexter Filkins, Hendrik Hertzberg, George Packer, and more of our coverage of Osama bin Laden’s death.