Rudy Giuliani has played a multitude of parts in public life: Tenacious federal prosecutor of the mob. Two-term mayor leading the revival of New York City—and consoler-in-chief when the city was attacked by terrorists. Giuliani has also been an enthusiastic drag queen and a failed Republican presidential candidate. Now he has taken on his least-likely role: spokesman for special counsel Robert Mueller. Unofficially, that is, but energetically and craftily. One week ago, Giuliani declared to CNN that Mueller had told him the special counsel “acknowledged” that a sitting president cannot be indicted. Three days ago Giuliani announced to The New York Times that Mueller’s timeline has the special counsel wrapping up the investigation into whether President Donald Trump obstructed justice by September 1. All of which may be true—or not. Hours after Giuliani’s most recent declaration, Reuters ran a story saying the September 1 deadline was “entirely made-up” by Trump’s new lawyer, attributing the pushback cryptically to a “U.S. official.” Mueller’s actual spokesman, Peter Carr, did what he has done for more than a year, however: quickly and politely decline to comment.

It may soon become much harder for Mueller’s office to maintain its silence as Trump’s team works to shape the political context for the results of the Russia investigations, and to destroy the special counsel’s credibility. Giuliani, for all his different guises, is at heart a politician, and one trained in the hand-to-hand combat of New York’s tabloid-media culture. So he has been quick to exploit a weakness in his current adversary. “There are serious Department of Justice rules and guidelines about what Mueller can talk about publicly, in regards to an open investigation,” says Mimi Rocah, a former federal prosecutor. “If there were a trial in progress and Giuliani tried to make these statements to poison the well or to influence jurors, a judge could issue sanctions. Giuliani’s getting away with it because there’s no pending court case right now. But it’s equally as problematic, if not more, because the jury pool here is the American public. And whatever else you can say, this whole strategy of calling it a witch hunt and attacking the prosecution is extremely effective with some part of the public.”

Mueller is not completely prohibited from responding to Giuliani—he could issue press releases to correct the factual record. And other special prosecutors have been much more talkative. When pursuing Bill Clinton, Ken Starr was a chatterbox to the media, for reasons both tactical and personal. Not yet 50, Starr was a man on the rise. “He cared about his image, his ambition, his media strategy,” said Lanny Davis, one of Clinton’s lawyers.

There are good strategic reasons for Mueller not to engage, however. “If Mueller responds to one thing, and then doesn’t respond to the next thing, does that mean the second thing Giuliani said was true?” Rocah says. Matthew Miller, a top Justice Department spokesman during the Obama administration, maintains an optimistic view of Mueller’s lack of visibility. “He has to worry about getting the facts right. And if he gets the facts right, when he releases them publicly, it will have enough of an impact that it won’t matter what Giuliani said in advance,” Miller says. “Mueller’s job is not to worry about the politics. The minute you start doing that, you start making mistakes. The best example of that is Jim Comey. Or maybe Ken Starr.”

Perhaps. Giuliani clearly recognizes that the Russia investigation is unfolding in a new media and political landscape where a lot of the norms don’t apply. Mueller’s keep-your-head-down, just-the-facts strategy is rooted in his own ascetic, disciplined personal style, and what is quickly becoming an antiquated tradition. His approach isn’t likely to change. But it isn’t oblivious to modern reality, either. “Oh, Mueller is critically aware of everything that’s being written or said. He reads his papers. He listens to the radio. He’s not missing anything,” a former top F.B.I. colleague says. “But he completely tunes it out. It’s a discipline. This is his way of flying above the fray, because once you get into it, you’re all in. There’s an old expression: ‘It’s like mud-wrestling with a pig. You’re both going to get dirty. The difference is that the pig likes it.’ But the very fact that Mueller refuses to respond to the most outrageous criticisms and claims is the reason the pig is wrestling with itself in its own mud.”

The former F.B.I. senior official recognizes something more substantive going on with his old boss as well. “This investigation is classic Mueller: he is doing a classic, organized crime case. This is RICO 101, working your way up and sideways. You pop a few guys for gambling, and no one is going to do a million years for gambling, but you’re gonna get their scratch pads, then you move on to their associates. You flip one guy who you arrest with no fanfare. It’s exactly what Mueller has been doing his whole goddamn life. It’s just that this time the boss of the family happens to be the leader of the free world. Mueller doesn’t care if he gets Trump. He doesn’t care if he doesn’t get Trump. He has no political agenda. He is digging through the layers and bringing back the truth, and the truth is going to be whatever it is going to be.”