To study voluntary control in conscious perception we exposed the visual system to an ambiguous stimulus that creates two states in neural processing that are governed by bi-stable perception rather than by the stimulus. In our paradigm observers estimated the orientation of a grid in 3D space. For specific combinations of monocular- and binocular-specified orientations observers were able to select either a monocular- or binocular-dominated percept and were able to flip at will between the two percepts in a well-controlled way. The perceived grid orientations were found to be well-described by a neural-population-code model in which both monocular and binocular signals contribute to both percepts.