Memory suppression is investigated in inhibition paradigms that produce cue-independent forgetting. Because the forgotten items are not retrieved even when tested with an independent, semantically related cue, it has been assumed that this forgetting is due to an inhibition process. However, this conclusion is based on comparing inhibition to classic interference theory with a single stage of recall. Yet, memory models, which produce forgetting through a process of interference, include both a sampling and a recovery stage of recall. A neo-classic interference theory is proposed, which assumes that interference exists during recovery as well as sampling and can explain cue-independent forgetting. Three behavioral studies tested predictions of the neo-classic interference theory. Experiment 1 found support for recovery interference in testing key predictions of the theory within the think/no-think paradigm. Most importantly, learning to quickly press enter produced as much cue-independent forgetting as no-think instructions. Experiment 2 tested the role of word frequency in terms of sampling and recovery, but failed to obtain cue-independent forgetting. Experiment 3 reversed the order of blocks and produced original cue forgetting following retrieval practice with independent cues, which provided a clear manipulation of recovery strength. Lastly, a mathematical model (SAM-RI) of neo-classic interference theory was specified that captures data from Experiment 1, Experiment 3, and is extended to the greater retrieval induced forgetting.