By Nyta Mann BBC News Online political correspondent

Happier days for Blair: The prime minister with Bill Clinton in 1997

It is still around, though in updated form; this weekend's Progressive Governance extravaganza, attended by heads of government and thinktankers from around the world, is the latest model.

But it is a third New Labour term and what to do with it, rather than the third way and what it means, that is at the forefront of Tony Blair's mind.

Record books

On 2 August his government succeeds Clement Atlee's as the longest-serving Labour administration. But after a sustained period on the back foot and with sympathisers wondering out loud whether his project has run out of steam, Mr Blair knows he needs to show he is doing more than just drifting into the record books.

The third way super-summit will, Downing Street hopes, provide a launchpad for that third term - and a kick-start to a rejuvenation.

But even its fans have to admit the third way isn't what it used to be.

When Tony Blair and New Labour began their march to power in the mid-1990s, it was the motif he chose to describe his party's modernised, neither-left-nor-right approach. Apart from stroppy lefties and library-stained academics, everyone wanted to wear it.

Bill Clinton, a key role model for early New Labourites, was in the White House. A wave of social democratic, centre-left governments had won office across most of Europe.

"What matters is what works" was a favourite phrase Mr Blair, and before long all his ministers, would repeat when faced with political objections to individual policies. He railed against ideology, preferring the measurable certainties of delivery and targets.

Baffles

Things are different now. In Germany, Gerhard Schroeder is engaged in a battle over employment reforms. The French socialists, never that keen on Mr Blair anyway, are in opposition. Italy and Portugal have seen their social democrats turfed out of office too.

Mr Blair's closeness to Bill Clinton's White House, meanwhile, has been superseded by a closeness to his right-wing Republican successor that baffles and alienates most of the European contingent attending the conference.

Add all this to the fact that no one was really quite sure what the third way was, and its failure to take the world by storm is hardly surprising.

But despite Peter Mandelson's dogged insistence that the third way is still alive and kicking, don't expect to hear ambitious Blairites chorus any such thing. And even Mr Mandelson himself, organiser of the conference, took the precaution of renaming it under the title "progressive".

Retreat

In recent days, Trade and Industry Secretary Patricia Hewitt has declared that focusing on "delivery" as if government were a take-away pizza parlour was a mistake.

An unchastened Peter Hain, the leader of the House fresh from his forced retreat over trying to open a debate about raising taxes, has bounced back to urge his colleagues to worry less about alienating Middle England and preach more about the values of liberty, social justice and redistribution.

Only last week Mr Blair himself admitted that, in harping on about "delivery" above all else, his government came across as "a bit technocratic, a bit managerial".

In other words, his government was failing to inspire or even get across to people just what it was for. Not unlike the third way, really.

With the conference intended to mark the start of the slog for that third term, mentions of the third way are likely to be kept to a minimum. "Progressive governance" is the new black.