A series of six experiments offers converging evidence that there is no fixed dominance hierarchy for the perception of textured patterns, and in doing so, highlights the importance of recognizing the multidimensionality of texture perception. The relative bias between vision and touch was reversed or considerably altered using both discrepancy and nondiscrepancy paradigms. This shift was achieved merely by directing observers to judge different dimensions of the same textured surface. Experiments 1, 4, and 5 showed relatively strong emphasis on visual as opposed to tactual cues regarding the spatial density of raised dot patterns. In contrast, Experiments 2, 3, and 6 demonstrated considerably greater emphasis on the tactual as opposed to visual cues when observers were instructed to judge the roughness of the same surfaces. The results of the experiments were discussed in terms of a modality appropriateness interpretation of intersensory bias. A weighted averaging model appeared to describe the nature of the intersensory integration process for both spatial density and roughness perception.