With the Egyptian-born Palestinian Arab terrorist Yasser Arafat either dead or dying, it’s past time for Washington to be thinking of what will come after. Two Arafat aides, Abu Mazen and Abu Ala, have each already failed in the role of Palestinian “prime minister.” That failure has been attributed to Arafat’s own interference, but it may also point to the risks of relying on Arafat cronies and members of what is called the Tunis crowd for the Palestinian Arab leadership. Which particular individual succeeds Mr. Arafat matters less than the principles by which the choice is made.

The first is that America has a role in helping those Palestinian Arabs who disavow terrorism, support freedom, democracy, and the rule of law, and accept Israel’s right to exist as a Jewish state in peace and within secure borders. There’s no reason to be bashful about this. Other regional actors, like the Saudis, Syrians, Egyptians, and Iranians, are supporting those in Judea and Samaria and Gaza who sympathize with their goals. America has no reason to stand on the sidelines instead of participating in making sure our allies among the Palestinian Arabs have the resources necessary to compete.

America would do well to avoid the trap of limiting the pool of acceptable new leaders to those who were part of Arafat’s gang. Arafat himself is heir to the tradition of hatred going back to Haj Amin el-Husseini, the so-called Mufti of Jerusalem, who sided with the Axis in World War II and spent part of the war in Berlin, plotting Jewish deaths in Palestine under the protection of Hitler, while the Jews were siding with the Allies. Arafat, according to one of the mufti’s biographers, Philip Mattar, was a relative of the mufti and was employed by him after the war, when Arafat was an engineering student at Cairo University. The Mufti, Mr. Mattar says, preferred the young Mr. Arafat to the Marxist George Habash.

As the responsible obituaries will make clear, Arafat never abandoned the mufti’s loathing of Jews and never really gave up terrorism, and he always put his own wellbeing and that of his cronies above that of his people. His aides are tainted by their association with him. The series of agreements America helped to be struck in the 1990s between Israel and the Palestine Liberation Organization after the secret meetings at Oslo can most charitably be seen as a failed test of the idea that peace could be won through negotiating with a terrorist organization, rather than with the non-Arafat Palestinians Arabs who had already been in negotiations with Israel at the Madrid conference when Mr. Arafat, fearful of being sidelined, held out his false offer of peace.

It was an experiment that led to the deaths of thousands of people. So there is a strong case for learning from the mistake rather than repeating it all over again. That means looking for Palestinian Arab leaders outside the PLO. Legitimacy for such leaders can not come from an anointment by outside powers but only from the democratic process, a free election in which a leader is chosen for a limited, set period. Whenever Mr. Arafat dies, there will be a new opportunity for the Palestinian Arabs to seize these principles in choosing for themselves a better leader. President Bush’s Rose Garden remarks in June of 2002 make it clear that he grasps these points more clearly than any American president before him.