This paper examines how observers estimate the overall orientation of spatially disorganised textures containing variable orientation. Experiments used asymmetrical distributions of orientations to separate the predictions from different models of average orientation estimation. Stimuli were composed of two spatially intermingled sets of oriented patches, each set having Gaussian distributed element orientation. The threshold separation of the means of the two sets was determined for a variety of tasks. Discrimination of these textures from a reference composed of two sets with the same mean orientation was well predicted by discrimination of orientation variability. A single interval judgement of which set contained more elements required a greater separation of the set orientations and suggested that the sets must be resolved in the orientation domain for independent representation of their properties. That resolution is required to perform this task further suggests that orientational skew is not coded. Threshold offsets for judgement of average orientation were re-expressed as shifts of four candidate features for coding the central tendency of texel orientations. Comparison with similar thresholds for single distributions of orientations indicated that average orientation is assigned to the centroid of a set of orientation measures.