Maintaining information in working memory often competes with concurrent processing of other information. This is reflected in the cognitive load effect, referring to the observation that processing tasks with a higher cognitive load result in lower memory performance. The cognitive load effect has been shown on many occasions in complex span tasks, which combine maintenance of memory items with a processing demand interleaved in between the presentation of the memory items. Two models of working memory, the Time-Based ResourceSharing (TBRS) model, and the Serial Order in a Box – Complex Span (SOB-CS) model, offer competing explanations for the cognitive load effect. Both lead to the prediction that a cognitive load effect should also be found in the Brown-Peterson task, in which the processing demand is inserted after the presentation of all of the memory items. Across three experiments, we show that (1) the cognitive load effect is consistently larger in the complex span task than in the Brown-Peterson task, and (2) the cognitive load effect is mostly absent in the Brown-Peterson task, with one exception. The current versions of the TBRS and SOB-CS models cannot account for these findings. We discuss what new assumptions are necessary for these models to explain our findings and consider alternative accounts explaining the current observations purely in terms of free time instead of cognitive load.