Just to reiterate what has been said, I learned in Machine shop 101, many years ago, that the secret to good countersinks is using an odd fluted countersink to eliminate harmonics that create chatter, in addition to using the correct cutting speed for the work at hand.
Properly lubricating the countersink, and possibly using cleaning patches, card paper, or toilet paper over the hole...in warm climates, can significantly improve the quality of one's countersinks.
J.D.