An exercise device having many advantageous features is described, including the ability to provide a variety of different accessory grips to the user, and the ability to easily mount the device to a wall. One exercise device described is an inelastic resistance device having integral hand grips. The accessory grips are removably attachable to the integral grip of an exercising device, and provide for gripping by the hands, foot or other body parts. The selection of a specific accessory grip allows the user to exercise by specific body parts and provides for a greater number of possible exercises. Accessory grips are attachable to the integral grips, greatly adding to the flexibility of the device. In addition, a novel hand grip is described having a plurality of cords that can be selected for gripping, and a bracket for mounting a door jamb mountable exercise device to a wall is described.