Odd things can happen when presidents no longer have to worry about re-election. George W. Bush (search) embarks on another four years in the White House unleashed from election concerns for the first time in his presidency, raising questions about what he will do with the freedom of a second term.

Past presidents have often reached big in their second term, with some accomplishments that build on earlier ones and others that can appear to contradict them. Regardless, with their eyes trained away from the voting booth and toward the history books, many have taken the chance to gamble.

Take President Reagan (search), who made fighting communism the hallmark of his presidency and famously proclaimed the Soviet Union the "evil empire" two years into his first term. But in his second term, Reagan seized on the ascension of Mikhail Gorbachev (search) to power and — despite rhetoric that remained fiercely hawkish — became friends with the Soviet leader and worked with him to steer their nations away from nuclear confrontation.

By the end of his presidency, Reagan had signed a treaty with Gorbachev eliminating the entire class of medium-range nuclear-tipped missiles. The combination of toughness and conciliation helped end the Cold War.

Or take President Clinton, the Democrat elected in 1992 after embracing his party's centrist movement. But it took him until the first State of the Union speech of his second term to utter one of the most famous quotes of his presidency — that "the era of big government is over" — and to tackle the historic welfare reform legislation that dismayed many in the left wing of his party.

Possibilities for a second-term Bush exist in part because of circumstances, and in part because of the agenda he has already set.

Either way, there's no disputing at least two things: He'll have lots of extra time now that he no longer has to devote time to raising money and campaigning for re-election. It also won't be long before attention will turn to the 2008 presidential contest and he'll be considered a lame duck.

White House political adviser Karl Rove said Bush in his second term "absolutely" would push for a constitutional amendment that says marriage consists only of the union of a man and a woman.

Bush believes states can deal with the issue of civil unions between gay people, an arrangement that if enacted would grant same-sex partners most or all the rights available to married couples, Rove said Sunday.

In foreign policy, one obvious opportunity is the Israeli-Palestinian conflict, as Bush's second term collides with changes in the region. Israel has taken steps to withdraw from Gaza after nearly 40 years of occupation.

With Palestinian leader Yasser Arafat hospitalized and gravely ill, the man seen by Washington as an untrustworthy peace partner may be sidelined.

Those developments could give Bush a chance to risk trying to make peace, and White House aides have already begun signaling they see an opening.

Observers also see a legacy-building opportunity in Bush's proposal to increase Social Security's long-term solvency by partially privatizing it. "He could really make his mark there," said Lee Edwards, an analyst of presidential decision-making at the conservative Heritage Foundation.

But to be successful on both those difficult fronts, Bush might have to curb the my-way-or-the-highway approach that has dominated his relations with Democrats in Congress and international allies, two groups whose help he will likely need.

"He's got political capital," said Princeton political scientist Fred Greenstein. "He'll have even more if he does some reaching out."

Greenstein suggested Bush may decided to do just that — fulfilling a promise he has made in the days since his successful re-election — by nominating "some kind of uniting figure" for any Supreme Court vacancy, instead of a conservative who would spark a bitter Senate confirmation fight.

However, experts noted there's been little indication from Bush that he plans to be anything other than the mostly unbending conservative of his first term. Since Election Day, he has promised to earn the trust of Democrats and talked of bipartisanship. But so far, that has mostly meant inviting Democrats to support his proposals and leaving them behind if they decline.

And in recent days, Bush has appeared, if anything, more emboldened than ever, political experts and presidential historians said. When asked to name his most immediate priorities, he raised an issue that is one of the most divisive flashpoints between the two parties — capping medical malpractice lawsuit awards.

"He talks the talk of conciliation, but he walks the walk of the solid conservative," said Allan J. Lichtman, a presidential historian at American University. "I see no sign the president is going to modify his approach."