A common treatment for operant problem behavior is alternative reinforcement. When alternative reinforcement is removed or reduced, however, resurgence of the target behavior can occur. Shahan and Sweeney (2011) developed a quantitative model of resurgence based on behavioral momentum theory that suggests higher rates of alternative reinforcement result in faster response elimination and greater resurgence when removed, whereas lower rates of alternative reinforcement result in slower response elimination but are followed by less resurgence. Thus, the present study was designed to examine whether faster target response elimination and less resurgence could be achieved by beginning with a high rate of alternative reinforcement and gradually thinning it such that a low rate is ultimately removed during a simulated treatment lapse. Results showed that high rates of alternative reinforcement were more effective than low or thinning rates at target response suppression but resulted in resurgence when discontinued. Low and thinning rates, on the other hand, were less effective at response suppression but target responding did not increase when alternative reinforcement was discontinued. The quantitative model cannot currently account for the finding that lower‐rate alternative reinforcement may not effectively disrupt behavior relative to an extinction only control. Relative advantages of high, low, thinning, or no alternative reinforcement are discussed with respect to suppression of target response rate during treatment, resurgence when alternative reinforcement is removed, and alternative response persistence, while taking into account differences between this animal model and modern applied behavior analytic treatments.