On Thursday, CNN reported a seemingly bombshell claim that Michael Cohen was in the room with several others when Donald Trump was told in advance of his son’s 2016 Trump Tower meeting with Russians promising dirt on Hillary Clinton. CNN, citing sources with knowledge, further reported that Trump approved of the meeting and that Cohen was willing to testify to special counsel Robert Mueller’s investigation to that effect. As stunning as this news might seem, if Cohen were to offer such testimony, it does not prove a crime on its own, and its impact depends heavily on other evidence, other witnesses, and later events. The case of obstruction against Trump is already strong without Cohen’s allegation, but Cohen could strengthen a growing case against Trump of conspiracy against the United States under 18 U.S.C Section 371.

It’s important to note that without knowing who CNN’s “sources with knowledge” are and what their interests might be, it’s difficult to assess this report. It’s similarly important to acknowledge that Cohen might not be the most credible witness in the world, even if the report is true. Any good prosecutor would be wary of presenting Cohen’s allegation by itself. Further, prosecutors might already have the key evidence that Trump Jr. told his father. The son made a phone call to an undisclosed number when he learned of the meeting. If prosecutors have already obtained the identity of the person who took Trump Jr.’s call, and if it was Trump, then Cohen’s allegation would be helpful but only marginally so. If Trump Jr. did not call his father, a prosecutor would want a second witness to corroborate Cohen’s allegation.

Also, on its own, it is probably not a crime for Trump to have known and approved of a meeting with Russians. Interpreting such a decision as a crime would be overbroad and would likely run into First Amendment problems, such as chilling effects on core political speech by candidates seeking information. When the reports of the Trump Tower meeting first surfaced, I wrote that such a meeting with Russian nationals for information—even “dirt”—should not be prosecuted as a felony under campaign finance laws that prohibit receiving a “thing of value” from a foreign national. I offered a hypothetical in which a newspaper published a fake document during the 2012 election purporting to be a Kenyan birth certificate for Barack Obama. Under such a stringent interpretation of campaign finance law, an Obama campaign official in that case might be prosecuted for traveling to Kenya to obtain the certificate, or for speaking with Kenyan officials about how to prove or disprove the authenticity of the certificate, as these might be considered a thing of value. I also noted what was perhaps a more apt hypothetical given this specific case:

[L]et’s say in the summer of 2016, a Russian official contacted the Clinton campaign with information that the Russian government was behind the hacking. Such information would be a “thing of value” to the campaign. Maybe the most appropriate reaction should be to direct the Russian informant to the FBI, but surely it would not be criminal for a Clinton official to meet with the informant to make sure to get the information as soon as possible.

Approving of the Trump Tower meeting, in and of itself, is not incriminating for President Trump, just as it wasn’t criminal for Trump Jr., Paul Manafort, or Jared Kushner to attend such a meeting. If the Russians had presented a thoroughly researched opposition file, that file would probably be “a thing of value” under a fair statutory interpretation and not just information protected by the freedom of speech.

Prosecutors would need to show more than just a meeting to prove such a conspiracy, but Trump has provided some of that evidence in broad daylight.

The real problem for President Trump would be any subsequent conduct that might point to a conspiracy to defraud the United States or to obstruction of justice. While “collusion” might not be a crime under any federal statute, any collusive conduct by the Trump campaign could be prosecuted as a “conspiracy against the United States” under 18 U.S.C. Section 371.

Mueller charged Manafort and Rick Gates under this statute for financial fraud against the Department of Justice and the Treasury Department, related to their alleged efforts to cover up lobbying work for a pro-Russian Ukrainian political party. Gates has already pleaded guilty to this charge. In 1924, the Supreme Court ruled that this statute covered schemes “to interfere with or obstruct one of its lawful government functions by deceit, craft, or trickery, or at least by means that are dishonest.” Former government fraud prosecutor Randall Eliason has explained how such conspiracy charges might be tried, citing a series of previous election-related cases. “Running a free and fair Presidential election is a core lawful function of the federal government,” Eliason wrote. “Any agreement to secretly and dishonestly attempt to interfere with a federal election would fall squarely within section 371’s prohibition on conspiracies to defraud the United States.”

Prosecutors would need to show more than just a meeting to prove such a conspiracy, but Trump has provided some of that evidence in broad daylight and on national TV. If Trump did know of the Trump Tower meeting, then his subsequent public statements encouraging Russian cooperation could be viewed as a signal to the Russians, particularly given that they seemed to actually follow through.

After receiving a request for a meeting with Russians promising dirt on Hillary Clinton, Trump Jr. responded with an email saying, “I love it” on June 3. On June 7, at around 5 p.m., he confirmed a meeting with the Russians for June 9 at Trump Tower. That same evening, Trump announced a “major speech” for the following week on “all of the things that have taken place with the Clintons.”

There was ultimately no major speech the following week, but we know now that soon after this chain of events, the Russians went into further action.

As Jennifer Taub observed following Mueller’s indictment earlier this month of 12 Russian intelligence officers accused of targeting the election through hacking efforts, the timing here is remarkable: on June 8, a day after Trump announced his planned speech, Russian agents allegedly launched DCLeaks.com and started disseminating their criminally hacked information. From this set of facts, it might be argued that Trump’s approval of the Russia meeting and his announcement of the Hillary speech might have sent an unmistakable public signal of cooperation, to which Russian agents responded by going public with their criminal anti-Clinton campaign.

If Trump recognized such a direct cause-and-effect link (approval of a meeting with Russians, followed immediately by criminal leaks of Clinton material), he would have reason to know that his public statements would trigger Russian cooperation. In that light, his public statement on July 27 is all the more damning: “Russia, if you’re listening, I hope you’re able to find the 30,000 emails that are missing.” As Mueller’s latest indictment alleged, Russian agents started a new round of spear-phishing directly targeted at Hillary Clinton’s personal office and the Clinton campaign that same day. This could all be used as evidence of a conspiracy to defraud the United States.

Moreover, if Trump knew of and approved the Trump Tower meeting, it would make all of the potential obstruction charges more concrete and powerful. It particularly would strengthen an obstruction case I identified last month in Slate: possible witness tampering of Trump Jr., specifically about the meeting itself. Trump’s lawyers acknowledge that he dictated to Trump Jr. a statement about the meeting, and that statement appears to be false, based on Trump Jr.’s emails and Manafort’s notes from the meeting.

If Trump dictated that statement, he might have been witness tampering not only for his son’s benefit—already a crime—but also for his own benefit—an even deeper one. He may have been putting his own son in criminal jeopardy to protect himself.

Ultimately, Cohen’s reported allegations, if uncorroborated by other witnesses or phone records, would be too risky for prosecutors to present on their own because of the potential witnesses’ own credibility problems. But if there are corroborating phone records or witnesses, then Cohen’s reported allegations could be a helpful piece of a criminal case directly against President Trump.

Read more from Slate:

• The Legal Case for Prosecuting a Sitting President

• Adam Schiff Blames Paul Ryan for Republican Efforts to Impeach Rod Rosenstein

• Why Kavanaugh’s Criticism of United States v. Nixon Should Worry Robert Mueller

• It’s Time to Accept How Unpopular Donald Trump Really Is