Emotional experiences create durable memory traces in the brain and tend to be incredibly well remembered. Importantly, moderate stress responses have been linked to increased performance on emotional memory tests, but suppressed ability to remember neutral information. Evidence suggests sleep also enhances memory consolidation, but the way stress affects sleep remains unclear. In the present study, participants encoded scenes of varying degrees of emotional arousal. After, participants completed a psychosocial stress task or a control task prior to sleep. Participants then completed a recognition task in which the objects and backgrounds were presented separately and one at a time. Stress subjects demonstrated an increase in memory for negative objects but poorer memory for their matched neutral backgrounds, resulting in a greater emotional memory trade-off compared to controls. Thus, HPA axis activation after encoding may 'tag' the emotional object as important to remember, enabling sleep to selectively increase memory consolidation while concurrently suppressing neutral information.