It is difficult to tell who is most desperate to get Ken Livingstone back in the Labour party - Tony Blair or Mr Livingstone himself.
Claims that this is a decision only for Labour's national executive, and the panel which will now interview him next month, should be taken with a lorry load of salt.
Mr Livingstone still speaks his mind
If Tony Blair did not want Mr Livingstone darkening his doorstep again, then there would not be a cat in hell's chance of him returning.
The fact is the prime minister is looking at the distinct possibility that, at a crunch election time for the government, his London mayoral candidate, Nicky Gavron, will come a poor fourth behind Mr Livingstone, Lib Dem Simon Hughes and Tory Steven Norris.
And that cannot be allowed to happen at the same time the government will be fighting elections in local councils and the European parliament.
What the prime minister wants most is victory, with London being run by a Labour candidate.
And the fact that nearly four years ago he did everything in his power to beat Mr Livingstone is neither here nor there.
Since then, apparently, Mr Livingstone has proved that he can run the capital successfully and not start a revolution from the Greater London Assembly.
He has even proved Mr Blair wrong on the congestion charge.
So, all can now be forgiven in the determination to have a winner on board.
Toe the line
John Prescott, Gordon Brown, Neil Kinnock and other senior Labour figures could not disagree more.
They believe Mr Livingstone is a one-man party who can do only harm to Labour. And they will do whatever they can to stop him being re-admitted.
But it is a pretty fair bet - if not a foregone conclusion - that Mr Blair will get his way.
Meanwhile, Mr Livingstone has made no bones about his desire to get back into the Labour party - to once again be "legit".
He has always seen his future in the Labour Party and will be delighted the London party has backed his readmission.
Ms Gavron could come fourth
At the same time, however, he has shown he is not ready to change his spots and offer too many pledges to toe the party line if he gets his way.
He recently infuriated his Labour enemies by describing George Bush as "the greatest threat to life on this planet that we've most probably seen".
And he has insisted that he is not about to change his views.
"I think both the prime minister and myself recognise we are not going to change each other, we have learned to accept each other.
"If I am the Labour candidate next summer it doesn't mean I am supporting the war against
Iraq, it won't mean he supports everything I say about President Bush," he said recently.
Of course, Mr Blair does not have a terribly impressive record when it comes to excluding troublemakers.
Falkirk's left-wing rebel Dennis Canavan was booted out of the party only to go on to beat the official Labour candidate in the election.
Rhodri Morgan was more-or-less blocked from becoming the party leader in the Welsh Assembly in favour of Blair favourite Alun Michael.
Mr Michael failed, resigned and Mr Morgan went on to take his place.
And there was Mr Livingstone himself who defied all Mr Blair's attempts to ensure Labour defeated him in the first mayoral contest.
Apparently nothing succeeds like success - or being a "labour" candidate opposed by the prime minister.