I didn't think there was too much smoke coming off the pan, but my fire alarm apparently disagreed. Luckily, it just makes a lot of noise, rather than calling the fire department. It took about five minute with the windows open for it to calm down and admit defeat.
I learned quite a while ago that the quickest way to get a smoke alarm to shut up is to wave a dish towel underneath it. Usually takes about 20 seconds to make the thing shut up that way.