Interactively creating and editing 3D content requires the manipulation of many degrees of freedom (DoF). For instance, docking a virtual object involves 6 DoF (position and orientation). Multi-touch surfaces are good candidates as input devices for those interactions: they provide a direct manipulation where each finger contact on the table controls 2 DoF. This leads to a theoretical upper bound of 10 DoF for a single-handed interaction. With a new hand parameterization, we investigate the number of DoF that one hand can effectively control on a multi-touch surface. A first experiment shows that the dominant hand is able to perform movements that can be parameterized by 4 to 6 DoF, and no more (i.e., at most 3 fingers can be controlled inde-pendently). Through another experiment, we analyze how gestures and tasks are associated, which enable us to discover some principles for designing 3D inter-actions on tabletop.