It is widely accepted that sleep aids in the encoding, consolidation and retrieval processes involved in memory processing, however, the conditions under which sleep influences memory may be substantially constrained. In a meta-analysis, we examined the effect that sleep has on both veridical (accurate) and false memory consolidation, in studies using the Deese-Roediger-McDermott (DRM) paradigm for memory of thematically-related words. The meta-analysis revealed that, whereas there was no overall effect of sleep on either accurate or false memories, the effect of sleep on memories was moderated by two constraints. First, sleep effects were influenced by the number of words within each themed word list, relating to differences in processing the associative network of related words. Second, sleep effects were greater in recall than recognition tests. Thus, whether sleep consolidation increased or decreased DRM veridical or false memory effects depended on specific features of the memory task.