Masked sentence perception by hearing-aid users is strongly correlated with three variables: (1) the ability to hear phonetic details as estimated by the identification of syllable constituents in quiet or in noise; (2) the ability to use situational context that is extrinsic to the speech signal; and (3) the ability to use inherent context provided by the speech signal itself. This approach is called "the syllable-constituent, contextual theory of speech perception" and is supported by the performance of 57 hearing-aid users in the identification of 109 syllable constituents presented in a background of 12-talker babble and the identification of words in naturally spoken sentences presented in the same babble. A simple mathematical model, inspired in large part by Boothroyd and Nittrouer [(1988). J. Acoust. Soc. Am. 84, 101-114] and Fletcher [Allen (1996) J. Acoust. Soc. Am. 99, 1825-1834], predicts sentence perception from listeners' abilities to recognize isolated syllable constituents and to benefit from context. When the identification accuracy of syllable constituents is greater than about 55%, individual differences in context utilization play a minor role in determining the sentence scores. As syllable-constituent scores fall below 55%, individual differences in context utilization play an increasingly greater role in determining sentence scores. Implications for hearing-aid design goals and fitting procedures are discussed.