Individuals with autism spectrum disorder (ASD) may mand repetitively for preferred items using the same mand topography, unless the environment is arranged to promote mand variability. For example, an individual with ASD may request access to songs played on the radio by repeating the word “dance” only. Previous research suggests that lag schedules of reinforcement can increase variability of vocal mands displayed by individuals with ASD. The current study evaluated the effects of a lag schedule of reinforcement and progressive time delay (TD) on the vocal mands by a 27-year old male, 28-year old female, and a 26-year old female. The evaluation included a multiple baseline across behaviors with embedded reversal design. A mand topography invariance assessment (MTIA) was conducted with each participant to identify new and existing vocal mand topographies. Two conditions were used to assess variable responding when variability was (Lag 1 + TD) and was not (Lag 0) required to produce reinforcement. During Lag 0, reinforcement was contingent on instances of independent manding (of any topography). During Lag 1 +TD, reinforcement was contingent on instances of independent variant and prompted variant responses (i.e., a mand topography had to be different from the mand topography that occurred independently in the preceding trial). A progressive TD was used to transfer stimulus control from an echoic prompt to naturally occurring contingencies. Results indicated that a Lag 1 schedule of reinforcement with progressive TD resulted in acquisition of novel vocal mand topographies for all participants, with varying effects on rates of independent variant mands. / Applied Behavioral Analysis