What next for Mr. Cohen? Based on the calculations in his plea agreement, he’s facing a probable sentence of between three and five years in federal prison. He undoubtedly wants to shorten that. His plea agreement is not a “cooperation” agreement. It does not explicitly require Mr. Cohen to help the government’s investigations, and the government does not promise sentencing credit for any such help.

But judges can, and often do, give credit for cooperation, and the government can always decide to recommend a lighter sentence later. And federal prosecutors clearly hope that Mr. Cohen will cooperate — his testimony that Mr. Trump directed his crimes was gratuitous unless prosecutors intended to lock him into that story for possible future use.

It’s clear that Mr. Cohen is cooperating in his own way. His lawyers have been foreshadowing that cooperation for weeks, suggesting their client wants to come clean about what he knows. His lawyer Lanny Davis was even more explicit: Just minutes after Mr. Cohen’s plea, he tweeted that Mr. Cohen had implicated Mr. Trump under oath, and asked: “If those payments were a crime for Michael Cohen, then why wouldn’t they be a crime for Donald Trump?”