His decision not to give public backing to any of the likely candidates for Labour's number two job removes the prospect of a campaign based on a 'dream ticket' theme.
But it also means that his candidature is likely to be balanced by a deputy drawn from the left or centre-left of the party. John Prescott, the employment spokesman, Margaret Beckett, the acting leader, and possibly Robin Cook, the trade and industry spokesman, are the most likely contenders.
The election of any of those three might serve to reassure 'traditionalists' within the party who argue that Mr Blair's vision is too bland.
The other main leadership contender from the 'modernising' wing of the party, the shadow Chancellor Gordon Brown, is highly unlikely to stand for the deputy position.
Some of those close to Mr Blair believe he may marginally prefer a Prescott candidacy, but one senior Labour source said yesterday: 'Any choice he makes creates problems - when you are out in front as he is, you do not need anyone else.' Instead, Mr Blair is expected to argue that the deputy's job is for the Labour Party, rather than him, to decide.
It also remains possible that there will be no contest for the deputy leadership, if Mrs Beckett decides not to challenge for the top job and is not challenged for the deputy job she has held for the past year.
Supporters of Mr Brown moved quickly to deny reports that he was considering an alliance with Mrs Beckett under which the acting leader would stand as his deputy.
Today Mr Brown will remind MPs and party workers that he remains in the race by making a speech outlining a new 'fairness agenda' and calling for a war on poverty.
He will also endorse Labour's backing for the European Social Chapter and argue that the key to economic success lies in a revolution in skills and personal development.
A poll by BBC TV's On the Record of 173 Labour MPs, MEPs and candidates in Labour-held seats will today show that Mr Blair has twice the support of his nearest rival in that part of the electoral college. The figures are: Mr Blair 38, Mr Brown 15, Mr Cook 14, Mr Prescott 6 and Mrs Beckett 5. The remainder did not answer.
Yesterday, in his first public comments on economic policy since the death of Mr Smith, Mr Blair said Labour would co-ordinate policies across Europe to secure sustainable growth.
It would also work to create a new European Recovery Fund to boost jobs and campaign for British adoption of the social chapter on fair treatment in the workplace.
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