A class of mathematical models of paired-associate learning implies that variation in the number of response-alternatives paired with a fixed number of stimuli will affect only the guessing probability. However, both Hilgard and Bower (1966) and Restle (1965) suggest that a two-response condition provides Ss with the opportunity to use a particularly efficient stratagem in which only the stimuli paired with one of the two responses are learned. The present study shows that the complexity of a model required to fit the two-response condition depends partly on whether Ss are instructed to use the efficient stratagem or are instructed not to use it. In the later case, parameter values were found to be invariant when eight stimuli were paired with two, four, and eight responses. Both frequency and latency data are considered.