It was their 10th meeting in three years and allowed Mr Clinton to attempt to give a hefty nudge to Mr Yeltsin's campaign bandwagon before June's presidential elections.
Mr Clinton, facing an election in November, warmly supported Russia's economic reforms, although he was careful not to go as far as Germany's Helmut Kohl, who has openly said he wants to see Mr Yeltsin stay in the Kremlin. Although the presidents hugged and complimented one another, and tried the odd joke, there was none of the backslapping merriment of the summit in New York last October.
Their discussions followed the G7 summit in Moscow on nuclear safety convened at the request of Mr Yeltsin, who has long harboured ambitions to join the leading industrialised nations, so far without success.
Although the two-day affair was marred by a domestic row over the death of 50 federal soldiers in a Chechen ambush, and overshadowed by Lebanon, it was not an outright disaster for Mr Yeltsin, and may even have allowed him to register some modest gains.
Above all, he managed not to commit any behavioural gaffes and although he seemed downbeat, he appeared in reasonable shape, and did nothing to heighten the lingering worries over his health which flared up last year with his second heart attack.
He berated his guests about Nato enlargement, which will have annoyed them but have gone down well with the electorate.
Yesterday Mr Clinton said his position on Nato was unchanged, but in no "way, shape or form does it mean a threat to the security or legitimate interests of Russia".
At a joint press conference, Mr Yeltsin even squeezed in some overt campaign sloganeering. Asked about his prospects of beating off a Communist challenge for the Kremlin, he retorted: "I'm not going to answer that, because I'm sure victory will be mine." This is disputed by Gennady Zyuganov, the Communist leader, whom Mr Clinton met last night. The Russian - who, rivals warn, will bring back Soviet-style Communism - told him he wanted "long-term, good-neighbourly and normal relations" with the US.
Mr Yeltsin also seized the opportunity to try to convince voters he is fulfilling his promise to end the Chechen conflict before the election. In remarks that will astonish recent visitors to villages in southern Chechnya, which have been bombed and shelled, he said there had been "no military operations" in Chechnya since 31 March: "It is another thing that some gangs are still there running around." Nineteen of Chechnya's 22 regions had signed peace deals, he said. But Chechnya "must and will" remain within Russia, a view Mr Clinton endorsed.
After their meeting yesterday, Mr Clinton said important progress had been made on the agreement on Conventional Forces in Europe, and the Anti-Ballistic Missile treaty. Russia has been accused of breaching the former by having too many troops in the Caucasus; the latter involves a dispute over the definition of the missiles covered under the treaty.
But as the flags and banners came down in Moscow, and the prostitutes - shooed away by the police while the G7 was around - begin to gather on the rain-swept Tverskaya Street again, Russians may well have been wondering whether they had witnessed much sound and fury, but nothing of significance.
G7's main agreements on nuclear safety contained no surprises and no historical advances. Even the agreement to have a complete ban on nuclear testing - perhaps its most significant achievement - depends on settling differences with China and India.
Mr Yeltsin has been told to raise the issue with Peking later this week, during his trip to China - another fixture which has as much to do with his efforts to be re-elected as with global affairs.Reuse content