Less than one degree? That's pretty fine. From 12:00 to 12:01 on my watch is 6 degrees.
I'm not sure on the detailed internals of servos, but you could roll-your-own servo control and calculate your own PWM pulses, I guess.
That's assuming you're using something more clever than a little £5 hobby-servo. Some of those rattle by more than what you're looking for 