How do humans combine the velocity information from two moving gratings (plaids) to detect pattern motion direction?-We are still unable to answer this question. The 'intersection of constraints' rule (IOC-Adelson and Movshon, 1982 Nature 300 523-525), and the 'vector average' rule (VA-Wilson et al, 1992 Visual Neuroscience 9 79-97) have both been supported by results in the plaid literature, but could these results be predicted by a 'squaring' nonlinearity that now forms part of several influential spatiotemporal energy models (Wilson et al 1992, loco cit.; Lu and Sperling, 1995 Vision Research 35 2697-2722; Simoncelli and Heeger, 1998 Vision Research 38 743-761)? Spatiotemporal energy in these models predicts directions other than those predicted by standard spatiotemporal energy models and may underlie the results that support the combination rules. The two combination rules and predictions from 'squaring' were tested under identical conditions. In the first three experiments a plaid was randomly presented in one of 45 different orientations, and observers were asked to remember the direction. The stimulus was then replaced by an oriented line indicating the direction predicted by one of the hypotheses. The observer was unaware which hypothesis had generated the line and was asked to make a same/different judgment. Results showed that the 'squaring' hypothesis was better at predicting perceived direction than either the IOC or VA.