Active physiological tremor compensation instruments have been under research and development recently. The sensing unit of the instruments provides information on three degrees-of-freedom (DOF) motion of the instrument tip using accelerations provided by accelerometers placed inside the instruments. A complete vector of angular acceleration of the instrument needs to be known to obtain information on three DOF motions of the tip. Sensing resolution of angular acceleration about the instrument axis is directly proportional to the width of the proximal-end sensing unit. To keep the sensing resolution high enough, the width of the unit has to be made large. As a result, the proximal-end sensing unit of the instruments is bulky. In this paper, placement of accelerometers is proposed such that the angular acceleration about the instrument axis need not be known to obtain information on the three DOF motions of the tip. With the proposed placement, the instrument is no longer bulky and fewer number of accelerometers is required, thereby making the instrument compact and better in terms of ergonomics and reliability. Experiments were conducted to show that the proposed design of placement works properly.