John Edwards offers boyish good looks and a trial lawyer’s verbal skills. Kathleen Sebelius is a heartland governor whose gender is another factor. And William Cohen provides political balance: He’s a Republican.

They’re part of a talented field talked up as entries in the John Kerry running-mate sweepstakes, each with something to bring to the Democratic presidential ticket. Although many Democrats want Kerry to name a running mate soon, their presumptive nominee doesn’t appear to be in any hurry.

Kerry’s selection process is unlikely to yield a decision for weeks. There are no firm assurances he will announce his selection before the nominating convention in late July, even though that’s the goal.

Heading Kerry’s selection process is Jim Johnson, a former chief executive officer for the mortgage lender Fannie Mae and a Democratic operative since he was a top aide to Vice President Walter Mondale.

Decisions on a running mate are made after careful political calculation. Still being debated is whether Kerry most needs regional, ideologic or ethnic balance for the ticket. Kerry refuses to discuss the issue and has made it clear he frowns on advisers who speak about it publicly, leaving many to talk only on condition of anonymity.

With the race for the White House tight, and with President Bush’s campaign already aggressively challenging Kerry, a quick decision could bolster fund raising and provide a prominent voice to counter Bush.

Potential running mates most often mentioned by Democrats are:

• Kansas Gov. Kathleen Sebelius. Adding gender balance to the list, she also is a moderate elected in a Republican state and could offer a bridge to groups like the Democratic Leadership Council.
• Rep. Dick Gephardt. The longtime Missouri congressman saw his bid for the nomination fade early, but he maintains strong ties to organized labor.
• North Carolina Sen. John Edwards. Kerry’s final major rival in the primary race is mentioned by virtually all after a relentlessly upbeat campaign that impressed many. Working against him is the difficulty of making an argument for change with two senators on the ticket.
• Bob Kerrey. The former Nebraska governor and senator is, like Kerry, a decorated Vietnam War veteran. Though he has impressed many with his work on the independent commission investigating the Sept. 11, 2001, attacks, Kerrey has said he’s not interested in joining the ticket.
• William Cohen. The Maine Republican served in the Senate, then as defense secretary under Clinton. His selection could be seen as a bold nod toward bipartisanship.
• Virginia Gov. Mark Warner. A fresh face after winning election in 2001, Warner could help in important Southern states. Like all governors, he has struggled with budget problems.
• New Mexico Gov. Bill Richardson. He would bring a nod to the nation’s largest and fastest-growing minority. A former U.N. ambassador, Richardson also would provide foreign policy experience.
• Iowa Gov. Tom Vilsack. He is in the middle of his second term in a state that narrowly went Democratic in 2000. He has left little doubt about his interest in higher office.