Although the motion of the line of sight is a straightforward consequence of a particular rotation of the eye it is much trickier to predict the rotation underlying a particular motion of the line of sight in accordance to Listing's law. Helmholtz's notion of direction-circle together with the notion of primary and secondary reference directions in visual space provide an elegant solution to this reverse-engineering problem, which the brain is faced with whenever generating a saccade. To test whether these notions indeed apply for saccades we analyzed three-dimensional eye movements recorded in four rhesus monkeys. We found that on average saccade trajectories closely matched with the associated direction-circles. Torsional, vertical and horizontal eye position of saccades scattered around the position predicted by the associated direction-circles with standard deviations of 0.5°, 0.3° and 0.4 °, respectively. Comparison of saccade trajectories with the likewise predicted fixed-axis rotations yielded mean coefficients of determinations (±SD) of 0.72 (±0.26) for torsion, 0.97 (±0.10) for vertical and 0.96 (±0.11) for horizontal eye position. Reverse-engineering of three-dimensional saccadic rotations based on visual information suggests that motor control of saccades, compatible with Listing's law, uses not only information on the fixation directions at saccade onset and offset but also relies on the computation of secondary reference positions that vary from saccade to saccade.