Last night, deputy attorney general Rod J. Rosenstein—the same Rod J. Rosenstein that Trump a week ago cited for his sacking of FBI director of James Comey—appointed Robert Mueller, a previous FBI director and close friend of Comey, to be special counsel overseeing the investigation into Russian election interference and “related matters.”

In the short term, this is something of a gift to the Trump administration. Questions about former national security adviser Michael Flynn and former campaign manager Paul Manafort, both of whom are reported to be key figures in the FBI’s investigation, can be sidestepped, as this matter is under investigation so the White House cannot be expected to comment. His investigation may stop Comey from testifying before congressional committees, at least in the very near future; in fact, it may give those committees license to tap the brakes altogether. And Mueller, like all special counsels, will proceed slowly and mostly in secret—think years, not months. So maybe they can get past this crisis and focus on the things they want to focus on: tax cuts, repealing Obamacare, etc.

In the long term, though, Mueller poses an existential threat to the Trump presidency. He has much to investigate—for starters, the possibility that Trump sought to obstruct justice by ending the Flynn probe likely falls within his “related matters” jurisdiction, for instance. From the administration’s perspective, the bigger problem with special counsels is that you don’t know where they’ll lead. White House and campaign staff will have to lawyer up. There are the possibilities of tangential scandals and perjury charges. There’s the likelihood that this will drag on into next year’s congressional elections, as stories about this or that person testifying before a grand jury or seeking immunity hit the front page.

For the public, there are some potential problems, too. The secrecy of the special counsel investigation, for starters. Mueller’s team probably won’t leak much, especially at the higher levels, so the information that gets out will likely be thin gruel. More important, Mueller will focus laserlike on questions of criminality.

As former George W. Bush speechwriter David Frum wrote recently in The Atlantic, this could impede a broader understanding of what actually happened, if it takes the place of other investigations.

I’m going to quote at some length, but it’s an important point:

Of all the types of independent investigation that have been suggested, a special prosecutor is the most likely to disappear down rabbit holes—the least likely answer the questions that needed to be answered. A select committee of Congress or an independent commission of nonpartisan experts established by Congress can ask the broad question: What happened? A select committee or an independent commission can organize its inquiry according to priority, leaving the secondary and tertiary issues to the historians. A select committee or an independent commission is not barred from looking at events in earlier years statutes of limitations. A select committee or an independent commission seeks truth.

A special prosecutor, by contrast, seeks crimes. The criminal law is a heavy tool, and for that reason it is thickly encased in protections for accused persons. The most important protection from the point of view of the Trump-Russia matter is the rule of silence. A prosecutor investigating a crime can often discover non-criminal bad actions by the people he is investigating. If those bad actions do not amount to crimes, the prosecutor is supposed to look away.

For a purely hypothetical example: Suppose a prosecutor were investigating a politician for alleged violations of election law. Suppose the prosecutor could not assemble sufficient evidence to justify an indictment—but did discover that the politician had received large financial assistance from organized-crime figures years before, beyond the statute of limitations. A responsible prosecutor would have to keep silent about that discovery. If it’s not a prosecutable crime, it might as well never have happened, from a prosecutor’s point of view.

On the other hand, if a prosecutor does encounter a prosecutable crime, that crime becomes a top-of-mind priority—no matter how secondary or tertiary the crime might seem in the larger scheme of things.

Meanwhile, the journalist Marcy Wheeler, who specializes in national security and civil liberty issues, argues that Mueller’s mandate is wholly inadequate.

As I read this [order], it covers just the investigation into ties between the Russian government and people associated with Trump’s campaign. Presumably, that includes Mike Flynn, Paul Manafort, and Carter Page, among others.

But there are other aspects of the great swamp that is the Trump and Russia orbit that might not be included here. For example, would Manafort’s corrupt deals with Ukrainian oligarchs be included? Would Flynn’s discussions with Turkish officials, or Rudy Giuliani’s attempt to excuse Turkey’s violation of Iran sanctions? Would the garden variety money laundering on behalf of non-governmental Russian mobbed up businessmen be included, something that might affect Manafort, Jared Kushner, or Trump himself?

Reporting from just last night illustrates how pertinent these sort of questions are: The New York Times’s reported that the Trump transition team—presumably including transition leader Mike Pence, now the vice president, knew Flynn was under investigation for being an unregistered foreign agent when it tapped him to be national security adviser. McClatchy’s D.C. bureau, meanwhile, reported that Flynn, after accepting more than a half-million bucks from Turkey, shut down a planned attack on ISIS in the city of Raqqa.

The decision came 10 days before Donald Trump had been sworn in as president, in a conversation with President Barack Obama’s national security adviser, Susan Rice, who had explained the Pentagon’s plan to retake the Islamic State’s de facto capital of Raqqa with Syrian Kurdish forces whom the Pentagon considered the U.S.’s most effective military partners. Obama’s national security team had decided to ask for Trump’s sign-off, since the plan would all but certainly be executed after Trump had become president.

Flynn didn’t hesitate. According to timelines distributed by members of Congress in the weeks since, Flynn told Rice to hold off, a move that would delay the military operation for months.

If Flynn explained his answer, that’s not recorded, and it’s not known whether he consulted anyone else on the transition team before rendering his verdict. But his position was consistent with the wishes of Turkey, which had long opposed the United States partnering with the Kurdish forces – and which was his undeclared client.

These reports are certainly worthy of investigation—one has to wonder about the judgment of an administration that gives such an important post to such a potentially compromised person—but don’t appear to be tied directly to Russia. Will Mueller get into them? Or is that beyond the scope of his charge?

All of this is to say that, while the appointment of a special counsel is a necessary and beneficial step, it is no substitute for a thorough, bipartisan, all-encompassing independent commission, or short of that, at least a series of diligent congressional inquiries. The special counsel gets at only part of the picture. The American public deserves the entire thing. So this shouldn’t be taken as an excuse for the various congressional committees—including the one chaired by North Carolina’s senior senator, Richard Burr—to back off. If anything, the public nears answers now more than ever.

For his part, Burr (along with ranking Democratic senator Mark Warner) has pledged that the Senate Intelligence Committee will indeed forge ahead:

The appointment of former FBI Director and respected lawyer Robert Mueller as special counsel for the Russia investigation is a positive development and will provide some certainty for the American people that the investigation will proceed fairly and free of political influence. The Senate Select Committee on Intelligence will continue its own investigation and to the extent any deconfliction is required, we will engage with Director Mueller and our expectation is that he will engage with the Committee as well.

And for his part, Trump will continue to be Trump.