Variations in prompt delay procedures are used in discrete-trial training to reduce the occurrence of errors before task mastery. However, the variations are seldom compared systematically. Using an adapted alternating treatments design, the present study compared progressive prompt delay with 2-s or 5-s constant prompt delay, on the acquisition of an expressive labeling task in four participants with autism spectrum disorder and intellectual disability. While all three prompt delay methods led to mastery of the tasks, albeit only when the tasks were simplified for one participant, progressive prompt delay generally proved the most efficient method on several measures, including lower error rates. This is consistent with the nature of the progressive prompt delay procedure which allows less time for errors to occur early in training. It is provisionally concluded that selection of progressive prompt delay is supported as a wise first choice option for clinicians, as a history of high error rates may impair later learning.