[pugs]

I agree, use center drills to start holes on the lathe.

Also check tailstock alignment. To do this take a piece of barstock as long as you can put between the tail center and about 3/8" in the chuck jaws. First short chuck it in the chuck and center drill for the center to run in. Then chuck by the last 3/8" (so the chuck jaws, aren't forcing the piece off at an angle) then take a light skim cut all the way across the piece (you can take a cut from each end be be sure and get the exact same dial reading). Then measure each end with a mic and check for the tail end being bigger or smaller then the chuck end.

If it is not the same on both ends then you will need to adjust the tailstock and recut the test piece until it is. This adjustment depends on your lathe style as to how it is done, but I usually throw a dial indicator on the tailstock body to be able to measure and read how much I actually moved it (move about half the difference of diameters)