Purpose: The goal of this study was to determine how various aspects of cognition predict speech recognition ability across different levels of speech vocoding within a single group of listeners. Method: We tested the ability of young adults (N = 32) with normal hearing to recognize Perceptually Robust English Sentence Test Open-set (PRESTO) sentences that were degraded with a vocoder to produce different levels of spectral resolution (16, eight, and four carrier channels). Participants also completed tests of cognition (fluid intelligence, short-term memory, and attention), which were used as predictors of sentence recognition. Sentence recognition was compared across vocoder conditions, predictors were correlated with individual differences in sentence recognition, and the relationships between predictors were characterized. Results: PRESTO sentence recognition performance declined with a decreasing number of vocoder channels, with no evident floor or ceiling performance in any condition. Individual ability to recognize PRESTO sentences was consistent relative to the group across vocoder conditions. Short-term memory, as measured with serial recall, was a moderate predictor of sentence recognition ([rho] = 0.65). Serial recall performance was constant across vocoder conditions when measured with a digit span task. Fluid intelligence was marginally correlated with serial recall, but not sentence recognition. Attentional measures had no discernible relationship to sentence recognition and a marginal relationship with serial recall. Conclusions: Verbal serial recall is a substantial predictor of vocoded sentence recognition, and this predictive relationship is independent of spectral resolution. In populations that show variable speech recognition outcomes, such as listeners with cochlear implants, it should be possible to account for the independent effects of spectral resolution and verbal serial recall in their speech recognition ability.