Speakers vary their speech rate considerably during a conversation, and listeners are able to quickly adapt to these variations in speech rate. Adaptation to fast speech rates is usually measured using artificially time-compressed speech. This study examined adaptation to two types of fast speech: artificially time-compressed speech and natural fast speech. Listeners performed a speeded sentence verification task on three series of sentences: normal-speed sentences, time-compressed sentences, and natural fast sentences. Listeners were divided into two groups to evaluate the possibility of transfer of learning between the time-compressed and natural fast conditions. The first group verified the natural fast before the time-compressed sentences, while the second verified the time-compressed before the natural fast sentences. The results showed transfer of learning when the time-compressed sentences preceded the natural fast sentences, but not when natural fast sentences preceded the time-compressed sentences. The results are discussed in the framework of theories on perceptual learning. Second, listeners show adaptation to the natural fast sentences, but performance for this type of fast speech does not improve to the level of time-compressed sentences.