Tomorrow is the 40th anniversary of the “smoking-gun” tape, a Watergate milestone: Richard Nixon, with the tapes rolling, ordered his staff to have the CIA tell the FBI to stop its investigation of the break-in — with the president himself suggesting that they use Watergate criminal Howard Hunt’s involvement in the Bay of Pigs as the pretext.

When that tape was revealed, two years later, it marked the final breakdown of the coverup — or, to be more precise, the coverup of the initial coverup, since Nixon had maintained throughout the Watergate investigations that he was never involved in plans to obstruct justice.

In fact, as famous as this tape is, its importance overall is mainly tied to the historical sequence of events in unraveling the conspiracy. What we know now, but what was still contested at the time, is that Nixon was thoroughly involved in the coverup more or less from the very start.

Yet the smoking-gun tape is still important because of what it tells us about the presidency in general. Because the bottom line of the White House order to “turn off” the FBI’s investigation was that, for the most part, it didn’t work.

Indeed, this all started even before we got to the June 23 plan. The president’s men had already been trying all week, without a lot of success, to get Attorney General Richard Kleindienst to severely limit the investigation (although they were quite successful at getting prosecutors to keep the White House informed of their investigation, which helped them, for example, script perjured testimony). The CIA gambit was sort of a last-ditch attempt to turn the probe off. It wasn’t a total loss; it bought the president’s men several days, which may have helped part of the trail go cold. But within two weeks, that had worn off and the FBI was back to its investigation.

Why is it important? It tells us volumes about the limits of presidential power. The president may be presented in the civics books as sitting at the top of a pyramid, with executive-branch departments and agencies below him, but in reality the people at the next level down, such as Cabinet secretaries, are also responsive to Congress and to the permanent bureaucracy below them. In short, that means that presidents cannot give them orders and assume they’ll be carried out.

Indeed, looked at through the lens of presidential authority, the roots of Watergate are all about the limits of presidential ability to get the bureaucracy to respond to presidents’ policy preferences. Nixon hired the “Plumbers” to operate out of the White House as part of his policy of harassing antiwar protesters and other political enemies precisely because the FBI refused to implement a White House plan to do that sort of thing.

Unfortunately for Nixon, this do-it-yourself way of bypassing the bureaucracy had its own costs (as Ronald Reagan found out later in the Iran-Contra scandal, which shared a White House insistence on using “presidential branch” operatives to carry out policies that regular executive-branch agencies were not doing). The result, for Nixon, was a presidency destroyed. But looked at from this point of view, the lessons from Watergate are not only the obvious ones of avoiding lawbreaking and paranoia, but more broadly applicable lessons about the proper limits of presidential power, and the consequences of trying to cheat those limits.

That doesn’t mean that presidents should simply accept their limited influence; to the contrary, effective presidents work hard to increase their influence over Congress, over the courts — and, yes, over the bureaucracy. But that takes hard work — what Alexander Hamilton famously called “energy in the executive.” It doesn’t come with the job. And it only works, Watergate tells us, if the president accepts that the inherent constraints of the office — and the other players in the policy-making system — are just as legitimate as the occupant of the Oval Office.