If, during training, one stimulus is correlated with a higher rate of reinforcement than another, responding will be more resistant to extinction in the presence of that higher rate signal, even if many of the reinforcers have been presented independently of responding. For the present study we asked if the response-independent reinforcers must be the same as the response-dependent reinforcers to enhance the response's persistence, Twelve Long-Evans hooded rats obtained 45-mg food pellets by lever pressing (variable-interval 100-s schedules) in the presence of two discriminative stimuli (blinking ys. steady lights) that alternated every minute during daily sessions. Also, in the presence of one of the stimuli (counterbalanced across rats), the rats received additional response-independent deliveries of sweetened condensed milk (a variable-time schedule). Extinction sessions were exactly like training sessions except that neither pellets nor milk were presented. Lever pressing was more resistant to extinction in the presence of the milk-correlated stimuli-is when (a) the size of the milk deliveries during training (under a variable-time 30 s schedule) was 0.04 ml (vs. 0.01 ml) and (b) 120-s or 240-s blackouts separated components. Response-independent reinforcers do not have to be the same as the response-dependent reinforcers to enhance persistence.