Scene layout and part assembly are basic tasks in 3D object manipulation. While movement methods based on 3D or 6D input devices exist, the most efficient 3D movement techniques are based on utilizing only two degrees of freedom. This poses the problem of mapping the motion of the 2D input device to efficient and predictable object motion in 3D. We present a new method to map 2D input to 3D motion in this paper. The object position follows the mouse cursor position closely, while the object always stays in contact with other surfaces in the scene. In contrast to existing techniques, the movement surface and the relative object position is determined using the whole area of overlap of the moving object with the static scene. The resulting object movement is visually smooth and predictable, while avoiding undesirable collisions. The technique also utilizes the fact that people easily recognize the depth-order of shapes based on occlusions. The proposed technique runs in real-time. Finally, the evaluation of the new technique with a user study shows that it compares very favorably to conventional techniques.