Don't bother centre drilling, centre drills are a throw back to when you used dead centres in a lathe and the pip is to hold white lead as a lubricant.

Unless you actually need a centre hole for a lathe, use spotting drills then the size drill or even better is to buy a few good quality stub drills and just use these to start and finish the holes, saves hours of time and being short and stubby they are hard to break