Last Tuesday, Michael Cohen, Donald Trump’s former lawyer, pleaded guilty to breaking campaign-finance laws by helping to pay two women, in the fall of 2016, not to disclose affairs that they’d had with President Trump. He claimed that he had made these payments at Trump’s behest, and that he had done so primarily to influence the Presidential election, which made his violation a criminal offense. Cohen’s plea has been hailed as the strongest reason yet to remove Trump from office, mostly because, unlike the other crimes of which several people in Trump’s circle have been convicted or accused, these particular acts were done in concert with the President. But the truth is that Cohen’s confession of a criminal motive does not necessarily establish Trump’s. In fact, a lifetime habit of behaving sleazily may very well help the President.

Cohen’s in-court statement made clear that, at Trump’s direction, he paid Stephanie Clifford, an adult-film actress whose screen name is Stormy Daniels, a hundred and thirty thousand dollars for her silence, far in excess of the twenty-seven-hundred-dollar limit that an individual may spend on a Presidential campaign, and that he helped get the National Enquirer to pay Karen McDougal, a former Playboy Playmate who also had an affair with Trump, a hundred and fifty thousand dollars to buy and suppress her story, in violation of the ban on corporate campaign spending. He also made clear that he engaged in this conduct in order to influence the Presidential election. Had he done it to protect Trump’s family or business, the same payments wouldn’t have been criminal—and, if he had gone to trial, it may have been difficult for prosecutors to convince a jury, beyond a reasonable doubt, that the election-related motive was the primary one.

Proving that Trump shared that motive will be a key factor in determining both the President’s legal jeopardy and the viability of impeachment proceedings. Many have assumed, given the context, that the evidence lies simply in Trump’s involvement. A tape, released in July, featured Trump discussing the McDougal payment with Cohen, and the Trump Organization reimbursed Cohen for his outlays. And, as Cohen’s attorney, Lanny Davis, tweeted, “If those payments were a crime for Michael Cohen, then why wouldn’t they be a crime for Donald Trump?”

But they might not be. Most people don’t want their extramarital affairs to become public, for family or business reasons, and a hush payment to a mistress is tawdry but often legal. One imagines that Trump, even before he ran for President, routinely had his lawyers handle payoffs to stave off damaging publicity. Earlier this year, Cohen said that that’s “what attorneys do for their high-profile clients.” “I would have done it in 2006,” he added. “I would have done it in 2011.”

The more that it can be shown that these kinds of payments were normal for Trump—rather than something extraordinary he did when he became a Presidential candidate—the more it would bolster his case. This is presumably why Rudy Giuliani, Trump’s current lawyer, has suggested, since May, that there was a “longstanding agreement” that Cohen “takes care of situations like this, then gets paid for them sometimes.” What would seem like a puzzling admission is likely part of a legal strategy to make the payments from 2016 seem indistinguishable from those that Trump has made for reasons other than winning an election. (This strategy might be undermined by the fact that payments offered for McDougal’s story became exponentially larger after Trump won the Republican nomination.)

Giuliani seems to understand the fine lines that constitute campaign-finance law. Trump, unsurprisingly, appears not to: he has claimed that there was no illegality because Cohen’s payments didn’t draw from campaign funds. Ironically, had the Trump campaign actually used such funds to make the payments, and disclosed the expenditures with a general but accurate description (“legal settlement,” for example), they would have been legal and perhaps gone unnoticed. Likewise, had Trump used his personal funds and disclosed the payments in a similar manner, that also would have been legal, since there are no federal limits for candidates’ expenditures on their own campaigns.

But Trump did not choose those options; he directed his lawyer to make the payments personally, with the assurance of reimbursement. The Department of Justice’s position that a sitting President cannot be criminally indicted means that Trump likely won’t face charges until, at the earliest, 2021. In the meantime, as he is tried in the court of public opinion, the question is to what extent Cohen’s plea will affect the public’s notion of Trump’s criminal liability. The meaning of “high crimes and misdemeanors,” the constitutional standard for impeachment, is not fully defined, and is as much subject to political will as to legal parsing. Commission of a crime is not necessarily an impeachable offense, and noncriminal wrongdoing could still be a basis to impeach. But a conclusion that the President has committed a crime would surely inform, and perhaps increase, the public’s willingness to support his removal.

Arriving at that conclusion, using only Cohen’s plea as evidence, may be tougher than it seems. In the past several days, it has become popular to call Trump an “unindicted co-conspirator,” which was the grand jury’s term for President Nixon’s role in the coverup of the Watergate burglary. In that case, the indictments of several other men for the crime of conspiracy made clear that Nixon was alleged to have conspired with them. (Conspiracy is the crime of at least two people agreeing to commit a crime, and cannot be committed by one person alone.) Had Cohen actually pleaded guilty to conspiracy, the Nixon analogy would work. Unfortunately, Cohen’s plea doesn’t offer the same clarity on Trump’s status as a co-conspirator, because the crimes Cohen pleaded to don’t require one. Even if we believe that Trump directed Cohen to make the payoffs, it is technically possible that Trump and Cohen did not have the same criminal intent. If Trump agreed to the payoffs chiefly for the purpose of sparing his wife and family embarrassment, he would be guilty of neither conspiracy with Cohen nor of the underlying campaign-finance crimes.

If Cohen’s plea is to alter the status quo, it will need to add up to more than the sum of its parts. Perhaps it will sufficiently disturb some members of Congress, or of the Administration, to spur meaningful pushback to this President’s defacement of our country’s legal institutions. Jeff Sessions’s vow, on Thursday, that “the actions of the Department of Justice will not be improperly influenced by political considerations” hopefully precedes a wider defiance of Trump in defense of the rule of law. It is also possible that, as Trump feels the walls closing in, he will behave in increasingly unstable and threatening ways, to a degree that finally convinces those around him that he is dangerously unfit to serve. However this nightmare of a Presidency comes to an end, we can hope only that the law will not be said to have been wholly ineffective.