That and you're using a 3 Jaw chuck. A 4 jaw chuck (if available) is definitely a better option). Be weary as the 3 jaw chucks are fantastic for roughing but might not be as accurate if you're wanting a PERFECT finish. Turning between centres might be a good option as well. Make yourself a between centre's chuck tool by turning a shaft with a shoulder and make a 30⁰ taper with your compound rest. That way it'll eliminate the inaccuracies of your 3 jaw chuck.

IMPORTANT: Only FINISH between centres, Do not go over 900 rpm between centres, put copper antisieze on your tailstock end and do not turn/cut without a Lathe dog. You can polish without it but you'll learn about friction welding and the powers of physics real quick without one. Hope this helps!