THE UNITED STATES and its allies have been working for months to remove Yemeni President Ali Abdullah Saleh from the multi-sided, bloody and increasingly anarchic political conflict in his country. Until Mr. Saleh fully yields the autocratic power he has wielded for the last three decades, there won’t be much chance of restoring order in a state that is becoming a key haven for al-Qaeda, much less of creating a new democratic order. So it is logical, on one level, that the Obama administration would be considering a request from Mr. Saleh that he be granted entry to the United States.

Still, the issuance of a visa to the Yemeni strongman would be a mistake. Without question, it would damage the U.S. image in Yemen and across the Middle East — especially among the mostly young protesters who are struggling to bring about a democratic transformation in their countries. It also seems much less likely to accomplish the aim of ending Mr. Saleh’s political machinations or of calming the streets of Sanaa, where pro- and anti-Saleh forces have been clashing.

Mr. Saleh agreed to a transition plan last month under which he would transfer authority to his vice president in exchange for immunity from prosecution. A new election for president is to be held in February. Supported by Saudi Arabia and the Obama administration, the deal offered a chance at ending months of domestic conflict. But while some opposition parties have accepted it, others — including much of the youth movement that started the revolt against Mr. Saleh’s regime this year — rejects it, because of the immunity provision.

On Saturday, government security forces, which are still controlled by members of Mr. Saleh’s family, fired on demonstrators who had marched to the capital in protest of the immunity deal. Later that day Mr. Saleh announced that he would leave the country for the United States — triggering what has been a conflicting flurry of statements from his government and the Obama administration.

In Washington, administration officials said Tuesday that they were considering allowing admission to the president for the sole purpose of obtaining medical treatment but had not yet made a decision. But in Sanaa, officials said they had been told by the U.S. Embassy that the visa had been approved and was unconditional. Mr. Saleh himself undermined the medical pretext, saying he was travelling “not for treatment, because I’m fine, but to get away from attention, cameras and allow the unity government to prepare for elections.” He added that he would return to join the “opposition” because “I won’t leave my people and my comrades.”

That suggests that Mr. Saleh’s departure would not end his political maneuvering. A visit to the United States could even bolster his standing, by implying continuing support from Washington. No doubt Yemen’s pro-democracy forces would interpret it that way — just as Iranian students were enraged when the shah of Iran was admitted to the United States for medical treatment in 1979. The U.S. ambassador to Yemen, Gerald Feierstein, has already damaged Washington’s position by publicly claiming that anti-Saleh demonstrators were trying to create “chaos.”

If Mr. Saleh really needs medical care — or his departure is desirable — Switzerland would make an excellent refuge. A U.S. visa would do more harm than good.