We discuss the origins and the suppression of the large frequency jitter on the carrier-envelope offset frequency (fceo) of fiber-laser frequency combs. While this frequency noise appears most prominently on f ceo, its effects are felt across the frequency comb and it is a potential limiting factor in applications of fiber-laser frequency combs. Here we show that its origin lies in the white amplitude noise of the pump laser output. We dramatically reduce this noise by operating the pump laser in a lower-noise state, i.e. at higher pump current, and by more aggressively feeding back to the pump current with an optimal feedback network. We demonstrate instrument-limited fceo linewidths and an integrated fceo phase jitter of 1 rad.