The former treasurer was back in the limelight yesterday, ostensibly to launch a colleague's new office but also to take a few questions on the leadership he publicly rejected the day after last year's defeat.

''Why won't you let your party and the Australian people know whether you intend to challenge for the leadership?'' he was asked.

''Well, I am not,'' he said.

Asked if that meant he was not challenging, he replied, ''Everyone knows that.''

There is speculation that Mr Costello wants the leadership handed to him without a fight just as he avoided challenging his long-time boss John Howard while in government. Whether he would accept it is another question.

Mr Costello's tell-all book is due out next month, when we are assured all questions will be answered.

He denied yesterday that he was putting publicity for that book ahead of his party's well-being.

But it means that, just as Dr Nelson is preparing a fresh assault on the Government in Parliament, which resume next week, his leadership becomes the focus once again.

He conceded yesterday that leading the Opposition could be a ''character-building experience'' at times, but said it was also an honour and a privilege.

''I am very determined and I will lead us to the next federal election.''

Dr Nelson had talked to Mr Costello about his future and said he would be very happy if he decided to stay.

''I'm reasonably confident I know [what he is going to do], but it's not my place to tell you,'' he said.

This latest talk comes after another poll, out this week, showed Mr Costello was the most popular choice to lead his party. Fairfax's Nielsen poll found Mr Costello was preferred by 44per cent of respondents. Dr Nelson was third, on 17per cent, behind his treasury spokesman, Malcolm Turnbull, on 27per cent.

It also comes as a new report points to another reason the Coalition lost power last year.

In an Australian Strategic Policy Institute paper, ANU political science professor Ian McAllister said Labor's increasing credibility on national security helped it win votes.

''On both defence and terrorism, Labor improved its position by a substantial 20percentage points; while it remained behind the Coalition, its disadvantage was small, and many more voters saw no difference between the major parties. Labor also benefited from the increasing unpopularity of the Iraq War and from its policy of withdrawing Australian troops.''

Again that may not come as good news for Dr Nelson, who was defence minister at the time.