Roc,
A lot of great advice from everyone so far. I've found that Dremel drills, at least the older models, don't hold a true center. Meaning the rotation of the drill "wobbles" even after I've provided a pilot hole first with a sharp dental pick and ensuring the bit is seated properly in the drill. I use a Ryobi 7.0 volt rechargeable cordless and it seems to be a lot more accurate. Also, the variable speed of the drill is regulated by how far I depress the trigger. I find I'm able to start out slow then I can pickup rpms gradually depending upon the material or the location of the hole. When I drill holes for pinning the assembled figure or mounting a figure to a base I usually use a power drill, but for detail work I always use a hand drill.
Take care,
Dave Neary