Summary: Three-dimensional (3D) projective structure, that is structure modulo a projectivity of 3D space, can be recovered from its projection in multiple perspective images. The images might be acquired, for example, by a moving monocular camera or a stereo rig. This projective structure can be upgraded to Euclidean, structure by identifying two entities, the plane at infinity and the absolute conic. Auto-calibration methods use constraints induced by the rigid motion of the camera to determine the Euclidean structure (or equivalently the camera calibration). Often these motion constraints are supplemented by known values of the camera's internal parameters or scene constraints in order to resolve ambiguities or stabilize the algorithms. It is shown in this paper that in certain common situations this supplementary information may not resolve the ambiguity. This is illustrated for the particular ambiguity arising for motions with a single direction of the rotation axis. Four types of constraint are analyzed, and the conditions under which the ambiguity is not resolved are given. The constraint cases are: perpendicular image axes (the zero-skew constraint); specified image aspect ratio; specified image principal point; and perpendicularity of scene features.