There has been growing interest in using adaptive training interventions such as Cogmed-RM to increase the capacity of working memory (WM), but this intervention may not be optimally designed. For instance, Cogmed-RM can target the primary memory (PM) component of WM capacity, but not the secondary memory (SM) component. The present study hypothesized that Cogmed-RM does not target SM capacity because the simple span exercises it uses may not cause a sufficient amount of information to be lost from PM during training. To investigate, we randomly assigned participants to either a standard (simple span; N = 31) or a modified (complex span; N = 30) training condition. The main findings showed that SM capacity did not improve, even in the modified training condition. Hence, the potency of span-based WM interventions cannot be increased simply by converting simple span exercises into complex span exercises.