Lag schedules of reinforcement have been found to be useful in addressing invariant behavior of individuals with autism spectrum disorder (ASD). The purpose of this study was to conduct an additive analysis of lag schedules and rules. Three participants with ASD were exposed to a Lag 2 schedule of reinforcement in isolation. Following, participants were introduced to an incomplete rule and then a complete rule regarding reinforcement in conjunction with the lag schedule. Results indicated that lag schedules in isolation were generally sufficient for increasing novel responding. The addition of incomplete and complete rules often resulted in increases, albeit small, in novel responding. Results are discussed in terms of applied use of lag schedules of reinforcement and addressing nonresponse.