After some toing and froing he ended up treating Paula Bennett – a former deputy Prime Minister - with sufficient respect to avoid a backlash from those within the National Party who regard Bennett highly.
Bennett was given a front bench seat with her ranking of 13, where she will sit sandwiched by the two MPs who did Muller's numbers: Bishop and Willis.
That could be a tad awkward, but the offer was respectable enough for Bennett to accept the offer.
Bridges rejected the offer of the Justice portfolio, and Muller rejected his request for Foreign Affairs.
Unable to settle on a portfolio, Muller simply left Bridges hanging.
Muller said Bridges had asked for time to consider his political future, but would be around the Cabinet table if he stayed and National was in Government.
That guarantee of a future Cabinet spot effectively meant any further demurring from Bridges would look like a tantrum.
Bridges is not stupid and quickly realised that.
He issued a statement by text to say he was not "considering his future" – he had already decided to stand again in the Tauranga electorate and was backing National to win in 2020.
Bridges will be given some time to lick his wounds, but if he does end up seething on the backbenches he may find he will be seething alone.
Muller has taken out insurance by giving Bridges' core supporters their preferred portfolios.
Critically, Bridges' supporters Michael Woodhouse and Todd McClay remain in their preferred portfolios of health and trade respectively.
Woodhouse was even promoted a smidgen, and Paul Goldsmith kept Finance. Mark Mitchell slots in at nine with Defence and Justice – the portfolio Bridges had rejected.
Muller has given them nothing to complain about. Only a foolish MP would put pique over a ministerial post.
Those decisions also make sense on merit. MPs should not be stripped of portfolios they are doing well in purely to reward a new leader's own supporters.
That was not just about trying to appease Bridges' camp. It was also because Muller intended to campaign on National's track record – the track record of the Sir John Key and Sir Bill English years.
Unlike Muller, many of those on the front bench were ministers under Key – and the faces of experience will be important in reminding the public about that track record.
The reshuffle also sees the resurrection of Amy Adams, who had said she would leave Parliament but has now changed her mind.
The creation of a specific over-arching Covid-19 portfolio for Adams was a clever move – beating Labour to the punch in having a dedicated portfolio and showing it will be the focus of National's campaign.
Further down the ranks the patronage is more obvious and potential quibbles lie.
Muller's supporters including Shane Reti and David Bennett were boosted well up the ranks, while Bridges' supporters Alfred Ngaro and Brett Hudson were cast down. They may feel hard done by.
But at the end that matters, there was little for Bridges' fans to complain about.
There have been teething problems for Muller – not least a spate of leaks of his staffing and reshuffle decisions before he was ready to announce them.
Muller will be hoping the reshuffle is enough to plug those leaks.