Complex (second-order) channels have been useful in explaining many of the phenomena of perceived texture segregation. These channels contain two stages of linear filtering with an intermediate pointwise nonlinearity. One unanswered question about these hypothetical channels is that of the relationship between the preferred orientations of the two stages of filtering. Is a particular orientation at the second stage equally likely to occur with all orientations at the first stage, or is there a bias in the "mapping" between the two stages' preferred orientations? In this study we consider two possible mappings: that where the orientations at the two stages are identical (called "consistent" here) and that where the orientations at the two stages are perpendicular ("inconsistent"). We explore these mappings using a texture-segregation task with textures composed of arrangements of grating-patch elements. The results imply that, to explain perceived texture segregation, complex channels with a consistent orientation mapping must be either somewhat more prevalent or more effective than those with an inconsistent mapping.