People often perform spontaneous body movements during spatial tasks such as giving complex directions or orienting themselves on maps. How are these spontaneous gestures related to spatial problem-solving? We measured spontaneous movements during a perspective-taking task inspired by map reading. Analyzing the motion data to isolate rotation and translation components of motion in specific geometric relation to the task, we found out that most participants executed spontaneous miniature rotations of the head that were significantly related to the main task parameter. These head rotations were as if participants were trying to align themselves with the orientation on the map either in the image plane or on the ground plane, but with tiny amplitudes, typically below 1% of the actual movements. Our results are consistent with a model of sensorimotor prediction driving spatial reasoning. The efference copy of planned movements triggers this prediction mechanism. The movements themselves may then be mostly inhibited; the small spontaneous gestures that we measure are the visible traces of these planned but inhibited actions.