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This study considered speech modified by additive babble combined with noise-suppression processing. The purpose was to determine the relative importance of the signal modifications, individual peripheral hearing loss, and individual cognitive capacity on speech intelligibility and speech quality.The participant group consisted of 31 individuals with moderate high-frequency hearing loss ranging in age from 51 to 89 years (mean = 69.6 years). Speech intelligibility and speech quality were measured using low-context sentences presented in babble at several signal-to-noise ratios. Speech stimuli were processed with a binary mask noise-suppression strategy with systematic manipulations of two parameters (error rate and attenuation values). The cumulative effects of signal modification produced by babble and signal processing were quantified using an envelope-distortion metric. Working memory capacity was assessed with a reading span test. Analysis of variance was used to determine the effects of signal processing parameters on perceptual scores. Hierarchical linear modeling was used to determine the role of degree of hearing loss and working memory capacity in individual listener response to the processed noisy speech. The model also considered improvements in envelope fidelity caused by the binary mask and the degradations to envelope caused by error and noise.The participants showed significant benefits in terms of intelligibility scores and quality ratings for noisy speech processed by the ideal binary mask noise-suppression strategy. This benefit was observed across a range of signal-to-noise ratios and persisted when up to a 30% error rate was introduced into the processing. Average intelligibility scores and average quality ratings were well predicted by an objective metric of envelope fidelity. Degree of hearing loss and working memory capacity were significant factors in explaining individual listener’s intelligibility scores for binary mask processing applied to speech in babble. Degree of hearing loss and working memory capacity did not predict listeners’ quality ratings.The results indicate that envelope fidelity is a primary factor in determining the combined effects of noise and binary mask processing for intelligibility and quality of speech presented in babble noise. Degree of hearing loss and working memory capacity are significant factors in explaining variability in listeners’ speech intelligibility scores but not in quality ratings.