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 the 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 this prediction to be wrong. In addition, we uncovered (1) that the duration of the processing episodes has no impact on the presence or absence of a cognitive load effect, and (2) that the duration of free time, a variable intimately tied to cognitive load manipulation, affects memory performance in the same way with and without a processing demand: Free time is beneficial for memory when inserted in between the presentation of the memory items, but not when added after the presentation of the entire memory set. These results imply that both current explanations of the cognitive load effect are wrong. We propose several alternatives to account for these results.