With John Roberts all but assured to bang the gavel when the U.S. Supreme Court returns to session next month, Republicans are now beginning to focus on the battle over the next nominee. That hearing is expected to make the one that just ended look like a high school mock trial by comparison, so whoever the nominee is will have to be tough. The next nominee will also be in danger of looking dim compared to the savant who stymied some of the most aggressive partisans in the U.S. Senate for nearly 20 hours last week without so much as a single note. He or she will have to be extremely sharp.

President Bush has not shown his hand yet. The only guidance he has given is to say he plans to case a “wide net” in choosing a replacement for Justice Sandra Day O’Connor. But few people think he will choose a male. The pressure to replace Justice O’Connor is not being driven by interest groups or the press, people close to the White House say, so much as it is by the administration itself. Some were surprised when the president nominated Judge Roberts to replace a woman. Even the president’s closest Republican allies will be shocked if he chooses a man this time around.

A federal appeals court judge for the Fifth Circuit, Priscilla Owen, is the favorite. She is a reliable conservative with a pleasant, homespun style that will play well in a hearing. Her most controversial opinion involved her defense of a Texas statute requiring minors who seek an abortion to notify their parents first. Because polls consistently show that a majority of Americans support such laws, the “extremist” tag is not likely to stick. She is close to Mr. Bush and his White House counsel, Harriet Miers, and, according to a veteran columnist, Robert Novak, met secretly with the president last week. She would be the least surprising pick.

Which is precisely why some people think the president will choose someone else. A source close to the White House said Mr. Bush plans to meet this week with a federal appeals court judge for the Sixth Circuit, Judge Alice Batchelder. Judge Batchelder would provide a sharp contrast to Judge Roberts, whose Ivy League education and comfortable upbringing became a sticking point for Democrats. She had a modest Ohio upbringing and graduated from Ohio Wesleyan University and from the University of Akron School of Law. She is erudite and well-read, but not lofty or aloof. And she is also old enough, at 61, that Democrats will not be able to fret, as they did with Judge Roberts, about her shaping the court for a generation.

The executive director of the pro-Roberts group the Committee for Justice, Sean Rushton, rejected the idea that Mr. Bush will choose someone at least 10 years older than Judge Roberts as a way of placating Democrats. “I don’t think it’s very complicated,” Mr. Rushton said. “The next nominee is going to be just like the last one. This is not Bill Clinton. This is someone who thinks big picture, who thinks principles, and who sticks to his guns.”

Others, though, said that the president has chosen older nominees for federal appeals court seats in California as a concession to that state’s two liberal senators, Senator Feinstein and Senator Boxer, and could follow the same route to avoid a meltdown from Democrats. Such a compromise would send a former U.S. solicitor general, Theodore Olsen, toward the top of the list. Other older possibilities along this vein would be a federal appeals court judge in California, Diarmuid O’Scannlain; or a federal appeals court judge who rides the Tenth Circuit, Paul Kelly.

Republicans criticized Democrats on the judiciary committee last week for questioning Judge Roberts about the quality of his heart. But Mr. Bush says he often makes decision on a gut feeling. A former deputy attorney general, Larry Thompson, could be the “gut” pick. The president is known to like Mr. Thompson, and his name bubbled up repeatedly during the hearing on Judge Roberts. Mr. Thompson, who is black, is a close friend of Justice Clarence Thomas. He could be a tough sell to the president’s base, since his credentials as a social conservative are something of a question mark.

Mr. Rushton said he doubts if anyone will be able to predict the president’s choice. But Mr. Rushton said he is certain that, despite popular sentiment, Republicans have little to fear in a strongly conservative nominee. The party has 55 seats in the Senate and can also depend on a handful of votes from Democrats in states that voted for Mr. Bush last year. “I’m convinced the next nominee will be a serious conservative,” Mr. Rushton said. “I think we have to realize they are going to yell and scream under any circumstances. If you know you’re going to have a fight, it might as well be a barn-burner.”