Recent research suggests that selectively attending to relevant stimuli while having to ignore or resist conflicting stimuli can lead to improvements in learning. While mostly discussed within a broader "desirable difficulty" framework in the memory and education literatures, some recent work has focused on more mechanistic questions of how processing conflict (e.g., from incongruent primes) might elicit increased attention and control, producing enhanced incidental encoding of high-conflict stimuli. This encoding benefit for high-control-demand or high-difficulty situations has been broadly conceptualized as a task-general property, with no strong prediction of what particular task elements should produce this effect. From stage processing models of single- and dual-task performance, we propose that memory-enhancing difficulty manipulations should strongly depend on inducing additional cognitive control at particular processing stages. Over six experiments, we show that a memory benefit is produced when increased cognitive control (via incongruency priming) focuses additional processing on the core meaning of to-be-tested stimuli at the semantic categorization stage. In contrast, incongruency priming targeted at response selection within the same task produces similar effects on initial task performance, but gives no memory benefit for high-conflict trials. We suggest that a simple model of limited-capacity and stage-specific cognitive control allocation can account for and predict where and when conflict/difficulty encoding benefits will occur, and may serve as a model for desirable difficulty effects more broadly.