While the influence of sleep on memory has a long history, sleep's role in the formation of false memories is less clear. False memory has been widely studied using the DRM task. Although technically a false memory, remembering the gist of experience is arguably an adaptive process. Recent studies demonstrate that a period of sleep benefits both true memory and gist-based false memory when compared to a wake period. Over longer delays (e.g. 1-2 weeks), true memory tends to deteriorate while false memory persists, but it is currently unknown how sleep influences this pattern. Here we assess how the positioning of sleep relative to memory encoding impacts later retention across longer delays of 24 and 48 hours. Participants encoded 16 DRM lists in the morning (WAKE 1st Groups) or evening (SLEEP 1st Groups), and were tested either 24 or 48 hours later at the same time (four groups). Results show that true memory was better after sleeping first, than after waking first. To a lesser extent, sleeping soon after learning also increased false memory. A negative correlation between SWS and false recognition was found, suggesting that SWS may be detrimental for semantic/gist processing. These findings are consistent with fuzzy trace theory, so that verbatim (true) memories are independent from gist (false) memories, and therefore, sleep can impact them differently.