The article deals with response rates (mainly running and peak or terminal rates) on simple and on some mixed-FI schedules and explores the idea that these rates are determined by the average delay of reinforcement for responses occurring during the response periods that the schedules generate. The effects of reinforcement delay are assumed to be mediated by a hyperbolic delay of reinforcement gradient. The account predicts that (a) running rates on simple FI schedules should increase with increasing rate of reinforcement, in a manner close to that required by Herrnstein's equation, (b) improving temporal control during acquisition should be associated with increasing running rates, (c) two-valued mixed-FI schedules with equiprobable components should produce complex results, with peak rates sometimes being higher on the longer component schedule, and (d) that effects of reinforcement probability on mixed-FI should affect the response rate at the time of the shorter component only. All these predictions were confirmed by data, although effects in some experiments remain outside the scope of the model. In general, delay of reinforcement as a determinant of response rate on FI and related schedules (rather than temporal control on such schedules) seems a useful starting point for a more thorough analysis of some neglected questions about performance on FI and related schedules.