Virtual trackball techniques are widely used when 3D interaction is performed through interfaces with a reduced number of degrees of freedom such as mice and touchscreens. For decades, most implementations fix a vertical axis of rotation, which is a suitable choice when the vertical axis should indeed be fixed, according to some mental model of the user. We conducted an experiment involving the use of a mouse and a touch device to study usability in terms of performance, perceived usability and mental workload when selecting different fixed axes in accordance with the user’s mental model. The results we obtained indicate that the consistency between the axis fixed by the technique and the object’s intrinsic axis has a positive effect on usability. We believe that implementations that allow to select different fixed axis for each specific object should be considered when designing future reduced-DoF interaction interfaces.