Is there opponency between orientation-selective processes in pattern perception, analogous to opponency between color mechanisms? Here we concentrate on possible opponency in second-order channels. We compare several possible second-order structures: SIGN-opponent-only channels in which there is no opponency between orientations (also called complex channels or filter-rectify-filter mechanisms); three structures we group under the name ORIENTATION-opponent; and finally BOTH-opponent channels which combine features of both SIGN-opponent-only and ORIENTATION-opponent channels but lead to predictions that are distinct from either of theirs. We measured observers' ability to segregate textures composed of checkerboard and striped arrangements of vertical and horizontal Gabor grating patches. The observers' performance was compared to model predictions from the alternative opponent structures. The experimental results are consistent with SIGN-opponent-only channels. The results rule out the ORIENTATION-opponent and BOTH-opponent structures. Further, when the models were expanded to include a contrast gain-control (inhibition among channels in a normalization network) the SIGN-opponent-only model was also able to explain a contrast-dependent effect we found, thus providing another piece of evidence that such normalization is an important process in human texture perception.