The compound-cue model of cognitive control in task switching explains switch cost in terms of a switch of task cues rather than of a switch of tasks. The present study asked whether the model generalizes to Lag 2 repetition cost (also known as backward inhibition), a related effect in which the switch from B to A in ABA task sequences is costlier than is the same switch in CBA task sequences. The model suggests that Lag 2 repetition cost should be absent from A'BA task sequences, in which A' and A are different cues for the same task. The cost is robust on such sequences, which suggests that cue-independent, task-specific representations are necessary for explaining task-switching performance and that the compound-cue model has limited explanatory power.