The lawyers and analysts, all of whom have been involved in directly or indirectly counseling the White House about Supreme Court selections, also said that because of Bush's desire to move quickly, he will likely choose from the roster of candidates whom he has considered before and whose backgrounds and records have been extensively researched.

The consensus among the handful of people who spoke about Bush's situation was that in addition to deciding whether he had the leeway to replace O'Connor with a male candidate, Bush will have to deal with other more pressing political questions in making his selection.

Among the questions: How much of his decision will be affected by a need to satisfy his conservative base, which shocked him with its widescale rejection of Miers? And how much of a political fight with Democrats is he willing to risk by naming someone in the mold of the conservative justices Antonin Scalia and Clarence Thomas?

One decision about any new nominee that seems beyond doubt is that Bush and his aides - and they awkwardly still include Miers on this issue - will select a candidate with unassailable legal credentials and a firm grounding in constitutional law.

One lawyer close to the President said that when Bush chose Miers he did so after concluding there was not a long roster of women candidates with whom he felt comfortable.

''When he chose her,'' said the lawyer, ''she was one of three finalists and the other two were men.''

The other two candidates, the lawyer said, were federal appeals court judges, Samuel Alito and J. Michael Luttig, both of whom remain leading candidates who would bring strong legal and judicial credentials to any confirmation battle.

Luttig has been at the forefront of the campaign to press a new conservative judicial approach, first as a senior aide in the Reagan administration, where he helped select candidates for the bench, and now as a judge on the 4th U.S. Circuit Court of Appeals, widely regarded as the boldest conservative appeals court in the nation.

As for women, Bush could select Judge Priscilla Owen of Texas, whom he recently appointed to the 5th U.S. Circuit Court of Appeals. Owen, whose record on the Texas Supreme Court established her as a strong opponent of legalized abortion, was confirmed to the federal bench in a compromise that ended a Democratic filibuster of her nomination.

She would also likely provoke a major political battle if Bush tried to name her to the Supreme Court.

Two other possibilities are Judge Diane Sykes of the 7th Circuit and Maureen Mahoney, who is not a judge, but someone whose profile resembles in many ways that of John Roberts, the new chief justice. Like Chief Justice Roberts, Mahoney has a strong academic record - she is a graduate of the University of Chicago Law School - and has argued many cases before the Supreme Court both as a deputy solicitor general on behalf of the government and for private clients as well.

As for naming a Latino candidate, which many of Bush's associates say he would like to do, he is largely prevented from selecting his most likely choice in that category, Attorney General Alberto Gonzales. In citing a reason for withdrawing Miers' nomination, Bush said he could not comply with the Senate Democrats' request for her work as his White House counsel because it would damage the ability of presidential advisers to give candid legal advice. As Gonzales was Miers' predecessor as White House counsel, the same issue would arise.