The ability of normal-hearing listeners to perceive sentences in quiet and in background noise was investigated in a variety of conditions mixing the presence and absence of periodicity (i.e., voicing) in both target and masker. Experiment 1 showed that in quiet, aperiodic noise-vocoded speech and speech with a natural amount of periodicity were equally intelligible, while fully periodic speech was much harder to understand. In Experiments 2 and 3, speech reception thresholds for these targets were measured in the presence of four different maskers: speech-shaped noise, harmonic complexes with a dynamically varying F0 contour, and 10 Hz amplitude-modulated versions of both. For experiment 2, results of experiment 1 were used to identify conditions with equal intelligibility in quiet, while in experiment 3 target intelligibility in quiet was near ceiling. In the presence of a masker, periodicity in the target speech mattered little, but listeners strongly benefited from periodicity in the masker. Substantial fluctuating-masker benefits required the target speech to be almost perfectly intelligible in quiet. In summary, results suggest that the ability to exploit periodicity cues may be an even more important factor when attempting to understand speech embedded in noise than the ability to benefit from masker fluctuations.