I was having a chat with an Opposition senator the other day when he expressed the opinion that the first thing the Prime Minister needed to do was "get a decent hair cut".

It was an unusual thing to hear.

Partly because I had assumed that the first thing he would have wanted Gillard to do was to swim solo out past Ashmore Reef to turn refugee boats around using only her teeth, or something.

And partly because - well, could you imagine how weird it would be if he had made the same comment a year ago, when the Prime Minister was Kevin Rudd?

I am sure that there is room for improvement in the PM's hairdo. There was room for improvement in her predecessor's.

Let's get something straight; politicians of both sexes get ribbed about their looks.

Most of them are martyrs to the cartoonists, who never waste the opportunity provided by a pointy nose or big ears, whatever the gender of the affected person.

(In fact, I would even argue that having an aberrant body part actually helps you in politics. If you have a giant schnozz or silly hair, you are absolutely likely to be cartooned more often, thus contributing to the impression that you are more central to proceedings than you actually are. People like Wayne Swan, who are so unmarked by genetic oddity that cartoonists are forced to draw them carrying briefcases emblazoned with their name, often wind up plagued by the perception of under-relevance.)

Tony Abbott gets flack about his ears, John Howard about his eyebrows, and Julia Gillard about her red hair and sharp nose.

Fair enough. But there is a huge difference between good-natured teasing about a distinctive physical characteristic, and the sort of thing that is happening to Julia Gillard.

And the difference is that for women, somehow, appearance turns into a competency issue.

Author and former Coalition adviser Niki Savva gave the PM a fairly robust serve this week, writing that the PM should "sack her hairdresser (sorry, Tim), get a decent cut and colour, pack up all her clothes and send them to the Smith Family. There are plenty of stylists who can buy her smart clothes that fit her properly."

Savva suggested that she get some exercise, too.

"If this all sounds gratuitous, it isn't. The photograph of Julia Gillard in Sydney's The Daily Telegraph yesterday, wearing a coat that looked as if it was made out of an army blanket by one of the infantry, said it all. How you look is as important as what you say and how you say it. And the rules apply equally to male and female politicians."

But I don't think that's actually true.

When men dress badly, it's a matter for fond reproach.

(Oh, Kevin. Those ankle-freezers! That bowl-cut!)

But when women dress badly, it's seen as a dark hint of further incompetence.

If she chooses a jacket of the wrong length, one shudders to think how she will build a national broadband network.

If she can't tweeze her eyebrows evenly, what hope is there that she can possibly legislate an appropriate carbon price?

Can you even imagine how annoying this sort of stuff must be for Julia Gillard?

Past behaviour tells us she is not especially precious about her appearance.

One wet, windy day years ago when she was out campaigning in her electorate, Gillard positioned herself in a gusty corridor outside a shopping centre, with card table and obligatory giant "Julia Gillard" placard.

The wind whipped her hair around and - red-nosed from the cold - she struggled to control her pamphlets.

An old bloke shuffled past, then stopped.

Turning, he looked at Gillard, then up at her poster picture, then back at Gillard.

"Taken on a good day, wasn't it love?" he cackled.

Gillard has told this story about herself with much enjoyment.

She has never been one for much makeup or fuss about clothes.

But now that she is Prime Minister, the popular gaze demands that she spend about an hour every working day being made-up, primped and polished.

This is an hour a day that her male colleagues and rivals don't have to spend, and which she - left to her own devices - probably would do almost anything to get out of. An hour a day which Kevin Rudd might have spent writing, or thinking, or phone-stalking Ban Ki-Moon.

An hour a day which could quite feasibly have been spent doing stuff that constitutes actual competence for a Prime Minister.

It must be uniquely frustrating to have to go through all that rigmarole and still be rubbished.

Especially in a week where she has managed to get a substantial piece of legislation through a nightmarish parliamentary system.

Especially when - truth be told - she actually looks just fine.

Annabel Crabb is ABC Online's chief political writer.