Drug addiction is a chronic relapsing disorder of compulsive drug use. Studies of the neurobehavioral factors that promote drug relapse have yet to produce an effective treatment. Here we take a different approach and examine the factors that suppress-rather than promote-relapse. Adapting Pavlovian procedures to suppress operant drug response, we determined the anti-relapse action of environmental cues that signal drug omission (unavailability) in rats. Under laboratory conditions linked to compulsive drug use and heightened relapse risk, drug omission cues suppressed three major modes of relapse-promotion (drug-predictive cues, stress, and drug exposure) for cocaine and alcohol. This relapse-suppression is, in part, driven by omission cue-reactive neurons, which constitute small subsets of glutamatergic and GABAergic cells, in the infralimbic cortex. Future studies of such neural activity-based cellular units (neuronal ensembles/memory engram cells) for relapse-suppression can be used to identify alternate targets for addiction medicine through functional characterization of anti-relapse mechanisms.