Knowing that a final agreement over Nato is well-nigh impossible, the United States has been pushing arms control up its agenda, saying that Mr Clinton has a package of concessions to make, particularly over the Start II missile treaty.
At present, the US has some 8,500 long-range warheads while Russia has between 6,000 and 7,000. The January 1993 treaty reduces the total for each side by half, to between 3,000 and 3,500. But it has been stalled as the Russian Duma - the lower house of Parliament - has failed to ratify it.
On the eve of the talks, the United States was offering a list of concessions. These included a delay by several years of the deadline for Moscow to blow up the silos in which missiles, banned under the treaty, are deployed; a delay on the Russian break-up of bombers and submarines, and a promise to drive the overall totals down to between 2,000 and 3,500.
But officials made it clear there was a condition: it would depend on Mr Yeltsin pushing the treaty, which was ratified by the US Congress last year, through his parliament this spring. The Russians may find this difficult to accept, although the wheelchair-bound Mr Clinton - who arrived in Helsinki accompanied by the chairman of his joint chief of staffs, Gen John Shalikashvili - appears to expect the offer to be taken seriously.
It is no easy task. The Russian legislature, which is dominated by Communists and Nationalists, is in an uncooperative mood, which has been deepened by outrage at the prospect of Nato moving up to Russia's borders. It has been further angered by the appointment of their arch-enemy, the economic reformer Anatoly Chubais, to the government.
There is also dispute over the deadline for Start II, which is supposed to come fully into effect by 1 January 2003. The Russians have been pressing for this to be pushed back. However, while being willing to move on the silos, the US has said it will not negotiate over a new deadline for warhead removal.
"What is key to us... is that we hold to the original Start schedule at least in terms of taking the warheads. It is the warheads that kill people," a US administration official told reporters.
They also floated the lure of a Start III treaty, which both Russian and US officials have been mooting for more than a month. This would set still lower ceilings on long-range missiles, although this is likely to depend on the ratification of Start II.