Sochi, Russia ? With time running out on an often testy seven-year relationship, President Bush and Russian President Vladimir Putin are taking on a lot of unfinished business in their final leader-to-leader meetings today.

The White House has ruled out chances of resolving differences over U.S. missile defense plans for Europe, but the two men hope to chart a course for better ties between Washington and Moscow after they leave office: Putin next month and Bush in January.

When they meet formally today, Bush will also have his first in-depth talks with Putin’s hand-picked successor, Dmitry Medvedev, who takes charge in Moscow on May 7.

The presidents were all jokes, smiles and handshakes when they greeted each other at Putin’s holiday dacha in this Black Sea resort before a lavish social dinner Saturday.

Yet behind what both sides say is a warm personal friendship, the list of contentious U.S.-Russia issues is a long one, even leaving out the missile shield dispute.

Russia’s vehement opposition to NATO’s eastward expansion into its backyard, divergent policies in the volatile Balkans, and U.S. complaints of increasing Kremlin authoritarianism and democratic backsliding will all feature on the agenda, officials say.

Still, Putin and Bush are expected to announce a new “strategic framework” to guide future U.S.-Russia relations in four broad areas: security, curbing the spread of weapons of mass destruction, counterterrorism and economic matters.

The document could include a reference to possible future cooperation on missile defense, but far less than what the Bush administration would have liked, especially after offering numerous concessions to ease Russian concerns with little success.

Russia fears the system, to be based in former Warsaw Pact nations Poland and the Czech Republic, is aimed at its nuclear deterrent. U.S. officials deny this and insist it is intended only to defend NATO allies from missiles launched by rogue Mideast nations, like Iran.

U.S. allies in Europe have sided with Bush on the matter and at last week’s NATO summit in Romania, alliance leaders fully endorsed the proposed system despite Russia’s objections.

At the same time, Russia is fiercely opposed to NATO’s enlargement into what was the Cold War-era Eastern bloc. Putin won a victory on that score last week, when NATO leaders put off opening the door to membership for Ukraine and Georgia, both former Soviet republics.

Bush had argued forcefully in favor of making the move now and even stopped in Kiev on his way to the NATO summit to assure Ukraine that he was fighting for it and Georgia.

Putin, however, convinced several NATO members, notably Germany and France, that the step would upset the balance of power in Europe, and Bush was forced to settle for a pledge that Ukraine and Georgia would eventually become part of the alliance.