Memory consolidation during sleep does not benefit all memories equally. Initial encoding strength appears to play a role in governing where sleep effects are seen, but it is unclear whether sleep preferentially consolidates weaker or stronger memories. We manipulated encoding strength along two dimensions--the number of item presentations, and success at visualizing each item, in a sample of 82 participants. Sleep benefited memory of successfully visualized items only. Within these, the sleep-wake difference was largest for more weakly encoded information. These results suggest that the benefit of sleep on memory is seen most clearly for items that are encoded to a lower initial strength.