Previous literature has identified several cognitive abilities as predictors of individual differences in speech perception. Working memory was chief among them, but effects have also been found for processing speed. Most research has been conducted on speech in noise, but fast and unclear articulation also makes listening challenging, particularly for older listeners. As a first step toward specifying the cognitive mechanisms underlying spoken word recognition, we set up this study to determine which factors explain unique variation in word identification accuracy in fast speech, and the extent to which this was affected by further degradation of the speech signal. To that end, 105 older adults were tested on identification accuracy of fast words in unaltered and degraded conditions in which the speech stimuli were low-pass filtered. They were also tested on processing speed, memory, vocabulary knowledge, and hearing sensitivity. A structural equation analysis showed that only memory and hearing sensitivity explained unique variance in word recognition in both listening conditions. Working memory was more strongly associated with performance in the unfiltered than in the filtered condition. These results suggest that memory skills, rather than speed, facilitate the mapping of single words onto stored lexical representations, particularly in conditions of medium difficulty.