Stimuli in one modality can affect the appearance and discriminability of stimuli in another, but how they do so is not well understood. Here we propose a theory of the integration of sensory information across modalities. This is based on criterion setting theory (CST; Treisman and Williams, 1984), an extension of signal detection theory which models the setting and adjustment of decision criteria. The theory of sensory integration based on CST (CST-SI) offers an account of cross-modal effects on sensory decision-making; here we consider its application to orientation anisotropy. In this case, CST-SI postulates that the postural senses are concerned with the relations between momentary body posture and the cardinal dimensions of space, vertical and horizontal, and that they also contribute to stabilizing perception of the cardinal orientations in vision through actions on the corresponding visual decision criteria, but that they have little effect on perception of diagonal orientations. Predictions from CST-SI are tested by experimentally separating the contributions that different information sources make to stabilizing the visual criteria. It is shown that reducing relevant kinaesthetic input may increase the variance for discrimination of the visual cardinal axes but not the obliques. Predictions that shift in the location of the psychometric function would be induced by varying the distribution of the test stimuli, and that this effect would be greater for oblique than cardinal axes were confirmed. In addition, peripheral visual stimuli were shown to affect the discrimination of cardinal but not oblique orientations at the focus of vision. These results support the present account of anisotropies.