The variations in intelligibility of a temporally interrupted connected discourse passage that result from changes in both switching conditions and message rate were studied. Six normal‐hearing listeners estimated the intelligibility of ten, 15‐sec speech samples presented monaurally at 36 interruption conditions (12 interruption rates × 3 speech‐time fractions) for each of two speaking rates. Results indicated that for a given speech‐time fraction, changes in intelligibility as a function of interruption rate depend on the precise temporal correspondence of switching and message parameters. Specifically: (1) for slow interruption rates, where on‐time and off‐time are greater than average word duration, temporal features of the message are relatively unimportant and intelligibility varies directly with speech‐time fraction; (2) intelligibility functions will begin to recover from minimum at an interruption rate where off‐time is equal to, or just shorter than, average word duration; (3) differences in performance along the recovery portions of the functions for the two message rates are negligible when intelligibility is expressed in terms of percent off‐time relative to average word duration. It is apparent that a trading relation exists between speech‐time fraction and interruption rate. Within certain limits, decrements resulting from lowering the speech‐time fraction can be overcome by increasing the switching rate.