Is the cookie sheet you're using really dark? Like, near black and old-looking? Because the metals in cooking pans blacken over time of use. And the darker it is, the more heat the pan will absorb, and the hotter the bottom of your cookies will become. It it's dark, instead of greasing it, put down a few pieces of parchment paper. Two or more if the sheet's REALLY black. I guess you can use wax paper too, I would think the wax would melt and make the cookies... Waxy. But I don't know, I've never used wax paper before.
The good thing about parchment paper though, is that you can reuse it many times. At least until it starts browning and getting crumbly.
The best thing to do is to watch the cookies closely while they bake.