When confronted with unfamiliar or novel forms of speech, listeners' word recognition performance is known to improve with exposure, but data are lacking on the fine-grained time course of adaptation. The current study aims to fill this gap by investigating the time course of adaptation to several different types of distorted speech. Keyword scores as a function of sentence position in a block of 30 sentences were measured in response to eight forms of distorted speech. Listeners recognised twice as many words in the final sentence compared to the initial sentence with around half of the gain appearing in the first three sentences, followed by gradual gains over the rest of the block. Rapid adaptation was apparent for most of the eight distortion types tested with differences mainly in the gradual phase. Adaptation to sine-wave speech improved if listeners had heard other types of distortion prior to exposure, but no similar facilitation occurred for the other types of distortion. Rapid adaptation is unlikely to be due to procedural learning since listeners had been familiarised with the task and sentence format through exposure to undistorted speech. The mechanisms that underlie rapid adaptation are currently unclear.