Albanese, a left fighter in the distant past, is the Prime Minister who looks for consensus where it's possible and useful, including with his opponent.

Dutton, who built a reputation as a head kicker of the right, as the Opposition Leader is seeking to reinvent himself as a more nuanced player, willing to negotiate when circumstances or interests demand or justify it.

Hence the two have met on the middle ground over the government's planned National Anti-Corruption Commission (the NACC).

Even before the legislation was introduced on Wednesday, the government effectively had Dutton's backing, coming out of direct discussions between him and Albanese.

One aspect on which they're in accord is the issue that's brought the sharpest negative reaction from critics: when the commission can hold public hearings.

The NACC would have open hearings only in "exceptional circumstances". That's the Victorian Independent Broad-based Anti-corruption Commission (IBAC) model, rather than the wider discretion given to the NSW's Independent Commission Against Corruption (ICAC).

Attorney-General Mark Dreyfus, saying NACC hearings would be mostly private, points out that's actually the case with ICAC - only 5 per cent of its hearings are public. (We might get a different impression because ICAC's public hearings have been so spectacular - think those involving Gladys Berejiklian.)

The government has taken on board the "reputational damage" public hearings can do, even before, or in the absence of, adverse findings.

Those wanting a less restrictive approach include a number of crossbenchers.

The small players might look more principled, but they also have less at risk. Among politicians, it's those in government (at present, and in the past and future) who are potentially most likely to be in the frame to face investigations.

The major parties have a common interest in putting limits on the circumstances in which there are public hearings.

Dreyfus says the government will look carefully at what comes out of the parliamentary inquiry into the legislation. He says he welcomes suggestions on who should head the commission, insisting the government doesn't have a name for the job.

Given the amount of power the commission will have, it is vital its head has bipartisan support.

That power will extend to whether and when it might look at "rorts" involving ministerial behaviour in grants schemes.

Dreyfus declines to be drawn on the NACC's remit here, saying "there's a spectrum in these discretionary grant programs." He refuses to say where the former government's sports rorts scheme might fall on that spectrum.

After the short parliamentary inquiry, we'll likely see a repeat of what happened on the climate legislation, when the government accepted crossbench tinkering - to be seen to be consultative - but did not make significant changes.

Dutton's effort to redefine himself is somewhat more sophisticated than when, launching a coup against Malcolm Turnbull in 2018 (which ended in Scott Morrison becoming leader), he talked about smiling more.

His supporters argue that in government Dutton was more flexible than he appeared, citing his drive for a solution on same sex marriage, but his public image was unrelentingly negative.

As leader Dutton is picking his fights (he opposed the government's climate legislation) while being willing to co-operate in some areas.

He's not going out of his way to defend certain aspects of the Morrison government, made easier by the fact he did not have a great deal of time for Morrison as prime minister.

He's also on the front foot with the media, despite much of it being rugged territory for him. He gave an interview for this week's Four Corners profile, which probably meant the program worked better for him than if he'd boycotted it.

It's notable that with the NACC Dutton declared a position ahead of the legislation going to the Coalition party room. Earlier, he'd acted pre-emptively on the climate legislation (for which he received some criticism internally).

While he has to be careful with the party room, Dutton is also in a strong position within his own side. He can't be too high handed - that could trigger white-anting. However the parlous state of the opposition frontbench means there are no credible challengers.

But both the attempted reinvention, and the challenge of bridging the broad divide within his own ranks, will be extremely difficult for him.

He is in a near impossible position in handling the government's referendum for an Indigenous Voice to Parliament. Opinions in the Coalition range across the board. A trenchant critic is new Indigenous senator Jacinta Price. There has been some speculation the opposition could adopt no formal position. That would reduce the referendum's chance of success but put less strain on Coalition unity.

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As it ended on Wednesday the last sitting before the October 25 budget, the government had every reason to be pleased with how Parliament is going. It has a number of main items from its election agenda introduced and some already passed. The NACC is set to go through in November.

It has the blessing of a benign Senate, where it needs the Greens and one more vote to pass contested legislation. The Greens are noisy critics and independent David Pocock, the progressive to whom the government looks for support, is politely vocal. But in the end, on most issues the pivotal votes in the Senate have nowhere else to go.

Politically, the government is travelling as smoothly as it could hope. But politics is only part of the story.

This week the OECD downgraded its forecasts for Australian and world economic growth next year, and those with mortgages braced for another interest rate rise next week. As welcome and important as the NACC reform is, those economic realities will be more front of mind for most Australians.