Temporal summation of the rewarding effects of medial forebrain stimulation in the rat was investigated by varying the interval separating the two short bursts of stimulation given as a reward in a runway. One finding--that the reinforcing effect of the two bursts is independent of interburst interval--supports a model in which there is perfect summation of the portion of the reward signal that exceeds some threshold. However, the constant-threshold form of this model is not reconcilable with the results of a second experiment, which shows that charge-duration functions obtained with different levels of performance differ by a multiplicative (scalar) factor, that is, the ratio between the values of the two functions is everywhere the same. (The charge-duration function gives the charge required as a function of the train duration.) None of the models of postsynaptic integration so far suggested is capable of explaining simultaneously the fact that the strength-duration function is a perfect hyperbola that has nearly reached its rheobase at a train duration no greater than 2 s, that there is no statistically detectable effect of interburst interval on summation between bursts separated by intervals up to 2 s and longer, and that the strength-duration functions (or, equivalently, the charge-duration functions) derived by using different performance criteria differ by a multiplicative factor.