Haptic perception is inherently active. People utilize different exploratory strategies that affect their perception. For example, people perceive small shapes more precisely when the finger explores them laterally as compared to anteroposterior, and they adjust their exploratory direction in a corresponding task to increase perceptual performance. Here, we investigated how prescribed movement direction of the finger affects texture perception and associated exploratory movements. Texture perception is based on spatial cues from static touch and temporal cues from active movement. We used stimuli that maximized the relevancy of movement-related temporal cues. The finger was moving lateral or anteroposterior to the body, but always orthogonal to the texture orientation. In addition, one group of participants explored while wearing a glove that further reduced the availability of spatial cues, another group explored without glove. Participants performed a two-interval forced choice task choosing in each trial the stimulus with higher spatial frequency. Participants applied higher force and stroked faster in anteroposterior orientation than in lateral orientation. Further, participants wearing gloves stroked the textures more slowly. Perceptual performance did not differ between conditions. We conclude that participants adapted their movement strategies to the respective exploratory constraints in ways to maintain good perception.