We investigated the role of spatial arrangement of texture elements in three psychophysical experiments on texture discrimination and texture segregation. In our stimuli, oriented Gabor elements formed an iso-oriented and a randomly oriented texture region. We manipulated (1) the orientation similarity in the iso-oriented region by adding orientation jitter to the orientation of each Gabor; (2) the spatial arrangement of the Gabors: quasi-random or regular; and (3) the shape of the edge between the two texture regions: straight or curved. In Experiment 1, participants discriminated an iso-oriented stimulus from a stimulus with only randomly oriented elements. Experiment 2 required texture segregation to judge the shape of the texture edge. Experiment 3 replicated Experiment 2 with Gabors of a smaller spatial extent in a denser arrangement. We found comparable performance levels with regular and quasi-random Gabor positions in the discrimination task but not in the segregation tasks. We conclude that spatial arrangement plays a role in a texture segregation task requiring shape discrimination of the texture edge but not in a texture discrimination task in which it is sufficient to discriminate an iso-oriented region from a completely random region.