Sleep strengthens declarative memory, but research investigating the effect of sleep on memory for information that is not explicitly studied for a test is sparse. In two experiments, we investigated the effect of sleep on gist-based and veridical representations of incidentally encoded information. Participants rated words from Deese-Roediger-McDermott (DRM) lists in either a deep or shallow encoding task and completed a surprise memory test after either sleep or wake. In Experiment 1, words were presented in lists, in order of descending associativity with the unpresented critical lure. Memory for list words and critical lures in both encoding tasks was stronger after sleep than wake, suggesting that sleep consolidated gist-based memory. In Experiment 2, the same words were presented in a random order across the experiment to minimize gist-based processing. Sleep strengthened veridical memory for list words following deep, but not shallow, encoding and did not affect critical lures. These results suggest sleep consolidates gist and veridical representations of information after incidental encoding, and that sleep-dependent consolidation processes may depend on processes at encoding, such as overlapping context and the strength of veridical memory traces.