Lag schedules of reinforcement require that reinforcement is made contingent upon a response differing in some dimension from previous n responses, though it has been argued that small lag requirements might produce higher-order stereotypy. In this study, 5 children from Hong Kong diagnosed with autism spectrum disorders (ASD) were required to vary their responding during a block-stacking task by lag-within (differing color within the structure) and lag-between (differing structures in an array) criteria, called lag-lag criteria. Data showed that the lag-lag criteria resulted in 2 of the participants passing all phases while 3 generally met lag-within but not lag-between criteria. Effects tended to generalize quickly to a picture identification task: I Spy. Post hoc statistical analyses support the results and give a foundation for assessing stereotypies in variability research. This study demonstrates how different lag schedule requirements might be effective in combating higher-order stereotypy in children diagnosed with developmental impairments and offers a unique approach to data analysis in lag-based studies. (PsycINFO Database Record (c) 2019 APA, all rights reserved)