The sleep-to-forget, sleep-to-remember (SFSR) hypothesis states that the neurobiological environment provided by rapid-eye movement (REM)-rich sleep decouples the content of an emotional memory from its attendant emotional arousal. This decoupling allows divergent attenuation and enhancement effects (i.e., erosion of the memory’s emotional tone and simultaneous strengthening of its content). However, support for this proposal is mixed. An alternative account suggests there might be convergent attenuation and enhancement (i.e., elevated emotional arousal is positively coupled with enhanced emotional memory). We tested predictions emerging from the SFSR hypothesis using (a) individuals diagnosed with post-traumatic stress disorder (PTSD; n = 21), (b) trauma-exposed non-PTSD individuals (n = 19), and (c) healthy controls (n = 20). We included PTSD-diagnosed individuals because they typically experience altered REM sleep, impaired emotional memory, and heightened emotional arousal in response to threatening stimuli. Participants were assessed before and after both an 8-h period of polysomnographically monitored sleep and an 8-h period of waking activity. The assessment included exposure to negatively valenced, positively valenced, and neutral pictures before the 8-h delay, and a recognition task afterward. We measured emotional arousal by recording psychophysiological responses to the pictures, both pre- and post-delay. Results indicated no significant between-group differences in emotional memory accuracy or arousal. However, after a sleep-filled delay, pictures of all categories were recognized with equal accuracy, whereas after a wake-filled delay, negative pictures were recognized preferentially. Furthermore, the findings demonstrated that a sleep-filled delay was associated with attenuated emotional arousal to pictures of all categories, whereas a wake-filled delay was associated with a rise in emotional arousal across the day. Intriguingly, poorer recognition accuracy for valenced (but not neutral) pictures was predicted by an interaction of increased REM fragmentation and increased emotional arousal. In summary, we found some support for the SFSR hypothesis in the way it describes the REM- and arousal-based mechanisms that process emotional material. We also, however, found disconfirming evidence regarding the outcome of that process (i.e., sleep did not favor consolidation of emotional over neutral memory), and we demonstrated a convergence between attenuation of emotional arousal and weakening of emotional content relative to neutral content.