Abstract In several papers, useful methods for deriving predictions of the Rescorla–Wagner (R–W) model were presented. This article supplements those previous efforts, which could not solve one important problem. Those cases are considered in which infinite solutions exist. In such cases, the resulting associative strength is determined by the initial associative strength. An important example is the experimental paradigm called relative validity. Surprisingly, an easy, pencil-and-paper solution can be derived. Based on the results of this paper, along with earlier ones, predictions can be derived for fairly broad conditions.