By Bridget Kendall
Diplomatic correspondent, BBC News
Tuesday's talks in Moscow were more positive than last October
Moscow says it has now received the proposals in writing it asked for from the Americans, aimed at allaying its suspicions that plans to base parts of a missile shield in Europe, allegedly to counter a potential Iranian threat, are really aimed at Russian defence installations.
So does this mean the escalating dispute between Russia and the US over this controversial missile system could be on the point of being resolved?
By their own accounts, talks this week in Moscow between US Secretary of State Condoleezza Rice and Defence Secretary Robert Gates and their Russian opposite numbers went rather better than the last round of talks in October.
On Tuesday, the Russian foreign minister even described the confidence-building measures outlined verbally by the Americans as "pretty serious and interesting".
That, presumably, is why the Russians wanted to see any proposals in writing. Russian officials say they will need several days to study the documents.
So what might be on the table?
Hints and speculation suggest the Russians are being offered monitoring access to the missile shield sites. What is not clear is what level of inspections would be allowed or how permanent any presence at the sites would be.
Nor is it clear whether other confidence-building measures are up for discussion.
Could a deal be cooked up on missile defence?
There have been reports of not activating the system without firm evidence of Iranian hostile intention - but who would decide that?
It is hard to imagine the Americans agreeing to anything that could look like a Russian veto.
But beyond the devil in the detail, there are, no doubt, political considerations.
This week's visit to Moscow was in part to try to iron out some bilateral tensions ahead of the Nato summit in Bucharest, Romania, in April, which both outgoing heads of state, Russian and American, will be attending.
The Russian press has been speculating that Vladimir Putin is unlikely to want to use this, his last major appearance on the international stage as Russian president, to lambast Nato allies.
George W Bush too, in his last few months as American president, would no doubt prefer to leave relations with Russia on an even keel.
That would be preferable to being remembered as the US president who left office with tensions with the old Cold War foe on the rise, and a major arms control treaty (the START arms pact, due to expire next year) left untidily unresolved, with no consensus on what should replace it.
And the Nato alliance as a whole could probably do without the prospect of a Russian rhetorical bombshell overwhelming the Bucharest summit.
Trying to get members to agree on Afghanistan deployments and on Nato's future purpose is surely challenging enough, without adding new tensions.
Quid pro quo
This has all led to further speculation: were talks in Moscow this week just about missile defence?
Or could a quid pro quo be being cooked up that would allow Russia to yield some ground on the missile shield question.
In return, the US - and Nato - would give way on that other East-West security issue that has the Kremlin mightily exercised: whether the former Soviet republics of Georgia and Ukraine might get a green light at Bucharest to begin formal accession to Nato.
Russia and the US are looking ahead to April's Nato summit
The Kremlin has repeatedly, over the past few weeks and months, in public and no doubt in private, made it clear that this is an issue it feels strongly about.
Of course, it is not surprising this sort of speculation should arise. Linking issues like this is an instinctive habit in Russia, where behind-the-scenes conspiracies are usually seen to be the rule not the exception.
And it is always tempting to contemplate grand deals that solve at one sweep a multitude of issues. Reality, though, is rarely so simple.
What does seem likely is that both sides - US and Russia - may be eyeing the political horizons ahead and calculating whether it is better to do a deal now, or make what appear to be conciliatory gestures while playing for time.
Moscow may well calculate that, whoever the next American president is, he or she may well be prepared to offer more concessions than George W Bush.
And Washington may also hope that the uncertainty of who will rule Russia from now on may provide new negotiating possibilities, and - who knows? - a more conciliatory President Dmitry Medvedev.
Neither assumption may be true. But it still could mean that both sides will play a longer game and, for all the speculation this week, no grand bargain will be clinched and the underlying disagreements will continue.