WASHINGTON — The new president decided that the international climate change agreement negotiated by his predecessor was a job killer that sacrificed American sovereignty. So he pulled the United States out while much of the world jeered.

For President George W. Bush, the withdrawal from the Kyoto Protocol in 2001 proved to be a seminal moment, cementing a perception of unilateralism that alienated overseas allies and further pushed away domestic critics. In the end, even his top advisers came to regret the move, not so much because of the merits of the decision, but because of the way it was handled.

Sixteen years later, another president has withdrawn from another climate change pact only to endure another chorus of catcalls from overseas. For President Trump, Mr. Bush’s experience offers cautionary lessons — some of which Mr. Trump and his staff seem to have internalized already, even though aides said they had not studied or thought much about the Kyoto precedent.

By coincidence, then, Mr. Trump, in moving away from the Paris accord, has taken steps to manage political fallout that Mr. Bush did not. Mr. Trump gave foreign allies, domestic advocates and his own advisers a chance to make their case directly to him before he made his decision. He announced the move openly, in front of the cameras, and explained his thinking. Immediately afterward, he called some of the more aggrieved foreign leaders to try to contain the damage. And he suggested that he was open to negotiating a new agreement.