Selecting and positioning objects in 3D space are fundamental tasks in 3D user interfaces. We present two new techniques to improve 3D selection and positioning. We first augment 3D user interfaces with a new technique that enables users to select objects that are hidden from the current viewpoint. This layer-based technique for selecting hidden objects works for arbitrary objects and scenes. We then also extend a mouse-based sliding technique to work even if the manipulated object is hidden behind other objects, by making the manipulated object always fully visible through a transparency mask during drag-and-drop positioning. Our user study shows that with the new techniques, users can easily select hidden objects and that sliding with transparency performs faster than the common 3D widgets technique.