Your new film, Damsels in Distress, is cult director Whit Stillman's first movie for 13 years…

Hold on, let me very quickly get my headset, so that I can do this interview without getting brain cancer. I just think it's bad to have your phone by your head. The WHO says it's carcinogenic, so when they say that, you listen, because they cured polio. [A short break.] Sorry, I'm a bit of a worrier. I spend a lot of time worrying about things like the fuel efficiency of helicopters. That's not something that I need to be worried about at this exact moment.

Do these fears impact on your life?

I'm not a reckless person with drinking, drugs or anything like that. I can't do anything that might result in death. I don't really like flying in planes. I'm not an overly cautious person, but you'll never see me on a motorcycle or jumping out of a plane with a parachute. That's not how I get my kicks.

Damsels in Distress is a comedy about a group of girls, led by your character, Violet, who attempt to civilise an uncouth American college. Would you agree it's an odd film?

Oh, it's very, very strange. It's a candy-coloured, musical, black comedy extravaganza. That's what it is. I went to a screening the other night and it made people really happy, and there aren't that many films like that now, that are kind of delightful. By the end, everyone's just smiling and I hope that's enough to spread the word and get people to go.

Whit Stillman is one of cinema's great eccentrics. Is it true that there was no swearing on set?

I tried not to swear because Whit doesn't like it. I wouldn't say I'm some hard-talking dame, but occasionally I would accidentally swear and he'd look over at me, horrified.

Would you describe yourself as eccentric?

I am completely so. I have also never placed a high value in fitting in. What's lucky is that I haven't found it to be a lonely endeavour. I've found plenty of other eccentrics.

Whit Stillman has been called "the Wasp Woody Allen". Now that you've worked with the real one, on his new film To Rome With Love, do you see similarities?

In a way, I find it strange that people put them together. I suppose they are both very funny and the characters who say their lines are smart and self-aware. But as film-makers, they are totally different. Woody Allen, for the most part, doesn't really want you to stick to the script. He doesn't need it to be word for word the way he wrote it, which is the opposite of Whit.

So Woody Allen is less precious about his words?

Oh, he's so not precious about his words, which is really strange. I always idolised him as a writer, and when he said: "Oh, just say whatever you want", I thought: "I can't say whatever I want. Woody Allen wrote this!"

You started out in "mumblecore" films such as Hannah Takes the Stairs and Baghead. Was it always your goal to work in studio movies?

I didn't have my sights set on anything in particular. I was barely two months out of college when I made Hannah and I was terrified. I didn't know how I was going to make a living. To say that what I really wanted to do was studio films, I don't think that would have even entered my mind. I think I was like: "I hope I find a way to get health insurance." I was working as a tutor and it wasn't until a couple of years into it that I was able to scratch out a living just doing acting. And part of myself is still scared that it'll all go away tomorrow.

Still? Bret Easton Ellis recently called you "probably the most interesting American actress in movies now".

Oh, entirely. I manage to figure it out from day to day and from job to job, but I don't think I will ever take it for granted or without gratitude. I've gotten wonderful opportunities, but I don't feel like everyone thinks I'm the second coming, which is a good thing because that's a recipe for either going crazy or failing.

One of your friends is actress and film-maker Lena Dunham, whose new TV show Girls is about to start. Is it a coincidence that you are both breaking through now or is the mainstream becoming more open to quirk?

Lena is a total genius and very, very funny – I got to read all the episodes of Girls before they shot them and you're going to love it, no question. But I also think that in my group of friends, we all had a bit of an indomitable spirit in so far as we were just going to keep making stuff. If this had not happened to Lena this way she would have continued to write and make her own stuff until someone took notice.

The only negative reviews you've had were for the remake of Arthur with Russell Brand. Did those hurt?

I really enjoyed working with him and I don't know why the press was so mean about that film. But what are you going to do? It happens. And it kind of made me feel very bonded with other actors. Even the actors you admire, nobody gets away with a perfect score. So it's comforting in a way. It makes you feel like you are one of the gang, like you've earned your stripes or something.

You've just shot a pilot of Jonathan Franzen's The Corrections for HBO with Ewan McGregor and Maggie Gyllenhaal. Surely that's too good not to happen?

Doesn't it seem like that? Call HBO and tell them that. We are waiting to hear what happens next but the pilot was wonderful and everyone is very talented, intimidatingly so.

You were a very good fencer as a teenager growing up in Sacramento, California. Could you have made the Olympics if you'd stuck at it?

I don't know. My problem was that even though I loved fencing, I've always been a performer at heart. But it was helpful for me. In competitive sports, you don't move more than you have to and everything is goal-directed. That's useful because the best acting is economical, it's not extraneous. People in life don't show extra emotions, unless they are trying to get something out of it. It's all about winning.