The baseline rate of a reinforced target response decreases with the availability of response‐independent sources of alternative reinforcement; however, resistance to disruption and relapse increases. Because many behavioral treatments for problem behavior include response‐dependent reinforcement of alternative behavior, the present study assessed whether response‐dependent alternative reinforcement also decreases baseline response rates but increases resistance to extinction and relapse. We reinforced target responding at equal rates across two components of a multiple schedule with pigeons. We compared resistance to extinction and relapse via reinstatement of (1) a target response trained concurrently with a reinforced alternative response in one component with (2) a target response trained either concurrently or in separate components from the alternative response across conditions. Target response rates trained alone in baseline were higher but resistance to extinction and relapse via reinstatement tests were greater after training concurrently with the alternative response. In another assessment, training target and alternative responding together, but separating them during extinction and reinstatement tests, produced equal resistance to extinction and relapse. Together, these findings are consistent with behavioral momentum theory—operant response–reinforcer relations determined baseline response rates but Pavlovian stimulus–reinforcer relations established during training determined resistance to extinction and relapse. These findings imply that reinforcing alternative behavior to treat problem behavior could initially reduce rates but increase persistence.