You probably remember this old joke. Question: How many psychiatrists does it take to change a lightbulb? Answer: Only one, but the lightbulb has to want to change. It's a punch line that comes to mind these days as President Bush fights the darkness by rearranging his team.

Bush is the eighth straight president, stretching back to Lyndon Johnson, who has tried to rescue his administration at a low moment by shaking up his staff. It has rarely worked, and on the few occasions when it has, the two crucial factors have been that the president has acted in time and, critically, has wanted to make fundamental changes.

We have not yet seen the end of the current reshuffling and should not underestimate Josh Bolten, the extremely capable new chief of staff. But these changes probably come too late, and so far, Bush seems to be acting only reluctantly, while remaining firmly opposed to instituting fundamental change.

President Johnson also acted halfheartedly and at the 11th hour, as the Vietnam War dragged on late in his presidency. He dispatched his defense secretary, Robert McNamara, to the World Bank and brought in a trusted outside heavyweight, Clark Clifford, who studied the war and decided it ought to be wound down. But there was too little time left, and Johnson, a captive of his own thinking, as Stephen Hess has written, made only modest changes in policy. A few months later, he withdrew from his race for re-election.

I was a young member of the White House staff when the Watergate break-in was reported in the summer of 1971. I continue to believe that if President Nixon had quickly come clean, overhauled his team and asked for public forgiveness, he would have still won re-election in 1972 and might have become a respected president. But instead he refused to change. He waited until 1973 to oust his chief of staff, H.R. Haldeman, and advisers like John Ehrlichman and John Dean. Even then, he was just tossing morsels to the wolves at the door. Some leaders are perhaps incapable of changing their core character and beliefs. That's a thought that gives pause today.

For one president, reshuffling his team actually backfired. Persuaded by his pollster, Pat Caddell, and in the face of skyrocketing gas prices and sagging poll numbers, President Carter retreated to Camp David in the summer of 1979 for 10 excruciating days to reflect on his troubles with the help of prominent leaders from outside his administration. He then came down from the mountain to deliver his famous "crisis of confidence" speech, also known as the "malaise speech," and propose bold new energy plans.

The public at first received the speech well, and President Carter's approval ratings improved. But the polls went into reverse a few days later when he fired half his Cabinet. Sensing that the president had lost control of his team and was desperate, the public gave him some of the lowest poll numbers of any president in modern times. Karl Rove has no doubt taken note.

Shaking up a team clearly worked, though, for President Reagan in 1986, when his administration was devastated by the Iran-contra scandal. Until then, Reagan had struck a deep chord of trust with the public; even people who didn't like his policies thought they could put their faith in him and liked him personally. The Iran-contra affair challenged that image with its suggestion of scandal and duplicity. The imbroglio sent his approval ratings plummeting into the 40s and even brought rumblings about impeachment.

Reagan's response to that situation could serve the current administration as a model of recovery. Not only did Reagan bring in an outstanding new team of outsiders — people like Howard Baker, Frank Carlucci, Ken Duberstein and Colin Powell — but he also swiftly changed the way he did business. Counseled by David Abshire, his special adviser on Iran-contra affairs, and others, he opened White House files to scrutiny, waived executive privilege so that Congress could interrogate anybody it liked, reached out seriously to Democrats and changed the tone in Washington. The road thereafter was not always smooth, but Reagan went on to achieve many of his goals at home and abroad, leaving office with an approval rating in the 60s.

President Clinton, too, was a leader who could change when things veered off course. I was a part of one of the Clinton shake-ups, joining the administration as his White House counselor when he was in trouble in the middle of his first year in office. Six months later, he had climbed out of the ditch and was on his way again.

It wasn't what I or others on staff did that ultimately made the difference. Rather, it was Clinton himself, with the support of his wife, Hillary. He acted early enough that he still had a reservoir of good will, and he made a genuine effort to alter the way he functioned.

Bush should have embraced the Reagan model of recovery last fall, when many urged it in the aftermath of Hurricane Katrina and the indictment of I. Lewis Libby. He had a decent chance to rebuild his presidency at that time. But he refused to change anything, choosing instead to "hang in" with the same policies, politics and personnel. Half a year has now passed, allowing the attitudes of those who were losing faith then to crystallize and harden.

The current shuffle is coming extremely late for a recovery — too late, probably — and so far, the administration has not brought in any outside heavyweights. The timing and nature of the shake-up signals that Bush's primary interest is in better management and marketing. Those will help, but they almost certainly will not be enough to rescue his presidency from its low approval ratings and loss of public confidence.

Bush has to want to change. He has to want to change policies like those on Iraq, energy and taxes; practices like secrecy; and politics like those that cater only to his base. Is he a leader whose resolve will ultimately become self-defeating stubbornness, or is he capable of flexibility, like his hero, President Reagan? Much rides on the answer.

David Gergen is a professor of public service and director of the Center for Public Leadership at the Kennedy School of Government at Harvard. He was a White House adviser to four presidents. He wrote this commentary for The New York Times.