Alcohol in perfumes?

I've viewed a few websites in search of an answer to whether alcohol is permitted in perfumes, trying to answer my friend's question. However, I can't find a definitive answer to this question; some people say it is strictly forbidden, while others that a seemingly arbitrary amount is halal in some perfumes. I've researched this before and it seems to hinge on whether alcohol is considered pure or not, but I never got to the bottom of that. So is perfume containing alcohol halal? Haram? If it's a grey area, under what circumstances is it considered one or the other?