Teleoperating a robotic hand with the aid of a sensorized glove presents some particular problems. A certain problem is due to the kinematic differences between the human hand and the robotic hand, which do not allow a simple direct mapping of the sensor readings from the glove to the robotic hand. This problem is addressed with different types of mapping, but none of them is of general use. This paper proposes two new mappings within two existing mapping types, as well as a new hybrid mapping that combines the best features of these existing mapping types. This hybrid mapping allows intuitive free space movements (where the gesture is more important than the precise positions of the fingers) and grasp movements (where the precise positions of the fingers is more important than the gesture), despite kinematic differences between the human hand and the robotic hand. The approach has been implemented, and some illustrative examples are presented in this paper.