Temporal contrasts in speech are perceived relative to the speech rate of the surrounding context. That is, following a fast context sentence, listeners interpret a given target sound as longer than following a slow context, and vice versa. This rate effect, often referred to as “rate-dependent speech perception”, has been suggested to be the result of a robust, low-level perceptual process, typically examined in quiet laboratory settings. However, speech perception often occurs in more challenging listening conditions. Therefore, we asked whether rate-dependent perception would be (partially) compromised by signal degradation relative to a clear listening condition. Specifically, we tested effects of white noise and reverberation, with the latter specifically distorting temporal information. We hypothesized that signal degradation would reduce the precision of encoding the speech rate in the context and thereby reduce the rate effect relative to a clear context. This prediction was borne out for both types of degradation in Experiment 1, where the context sentences but not the subsequent target words were degraded. However, in Experiment 2, which compared rate effects when contexts and targets were coherent in terms of signal quality, no reduction of the rate effect was found. This suggests that, when confronted with coherently degraded signals, listeners adapt to challenging listening situations, eliminating the difference between rate-dependent perception in clear and degraded conditions. Overall, the present study contributes towards understanding the consequences of different types of listening environments on the functioning of low-level perceptual processes that listeners use during speech perception.