"You can't get a man with a gun ..."
Even if you have the voice for it - as Williams certainly does - you do not get to be headlining a top musical if you are not prepared to make some difficult choices, take risks and push yourself to tackle new challenges. Ever since she made her West End debut at 18, playing Truly Scrumptious opposite Michael Ball in Chitty Chitty Bang Bang, Williams has been doing just that.
Back then, she had a place lined up at Heriot Watt University, Edinburgh, to study languages "but they agreed to let me put that offer on hold for a year. And then another year ..."
Williams, by now, is laughing. Because as her extensive CV shows, the 31-year-old has paid her dues in Edinburgh - but on the Fringe, not in the lecture room.
In a way, however, the Fringe was itself a learning curve. Williams merrily recalls the hugger-mugger adrenalin rush backstage in a venue where 10 shows a day were jostling for wardrobe space, and having to get on stage (and off) against the clock. "You learn not to leave vital props or bits of costume lying around," she says. "Because it won't necessarily be there when you go back - usually minutes before your show goes up! It's funny now, looking back at those kind of panics, but it does teach you to be organised and responsible. It is not very glamorous, but it is the kind of training you can only get when you are on the job."
On this current job, however, Williams discovered she would need other kinds of training if she was to play the sharp-shooting Annie opposite Jason Donovan - he is Frank Butler, the man she has in her sights (whose own eye is on the ladies in frills and lace, not backswoods buckskins). First up: how to handle a gun.
"I had not had to use one before," says Williams, "and as Annie I had to make it look as if I really was the hot shot who could do tricks with a Winchester." Had she read the small print in her contract, she would have realised some of those tricks had to be done from a trapeze. Williams is terrified of heights.
In Chitty Chitty Bang Bang, she plea-bargained with herself it was really the car that flew out over the auditorium stalls- she just happened to be sitting in it at the time. But in Annie Get Your Gun, the toe-curling episode would see her in full view of the audience and in a tight-fitting, spangly costume and carrying a rifle.
"Normally, you wouldn't get me up a ladder, not even a little one," says Williams. So how did she get round this? "I did trapeze classes. About a week before rehearsals, I got on a flying trapeze and learnt how to do tricks. In your head, you are thinking 'am I mad?' But then you start thinking not just about the show and how much you really want to do it. You think about Annie Oakley herself, what she achieved in what was essentially a man's world. So you get on a flying trapeze, somersault through the air at 40 feet - and don't die, after all.
"It's still scary, hanging by your legs, looking out over the audience and having to handle the gun correctly - but it's worth the bruises and white knuckles!"
Williams also relishes the musical challenges in the Irving Berlin score - not least that long, high note that caps that show-stopper duet Anything You Can Do, which Williams holds brilliantly from within the confines of a corset. "That has made me extend my whole vocal range again. I am classically trained as a soprano, but have tended to settle into being a mezzo - now I'm back up the scale again, and loving it."
There doesn't seem to be a downside that Williams is unable to flip over into something positive. Time on her hands offstage? Oakley apparently did needlepoint, while Williams studied for an Open University degree.
"It took me six and half years, but last year I graduated with a BA in English Literature - so my brothers can stop acting superior about their degrees, now." Anything they can do, she can do better!
Annie Get Your Gun is at the Playhouse, Edinburgh, from tonight to Saturday and at Theatre Royal, Glasgow, September 2-6 and His Majesty's, Aberdeen Sept 16-20.