Purpose: Amplitude compression is a common hearing aid processing strategy that can improve speech audibility and loudness comfort but also has the potential to alter important cues carried by the speech envelope. In previous work, a measure of envelope change, the Envelope Difference Index (EDI; Fortune, Woodruff, & Preves, 1994), was moderately related to recognition of spectrally robust consonants. This follow-up study investigated the relationship between the EDI and recognition of spectrally sparse consonants. Method: Stimuli were vowel-consonant-vowel tokens processed to reduce spectral cues. Compression parameters were chosen to achieve a range of EDI values. Recognition was measured for 20 listeners with normal hearing. Results: Both overall recognition and perception of consonant features were reduced at higher EDI values. Similar effects were noted with noise-vocoded and sine-vocoded processing and regardless of whether periodicity cues were available. Conclusion: The data provide information about the acceptable limits of envelope distortion under constrained conditions. These limits can be used to consider the impact of envelope distortions in situations where other cues are available to varying extents.