Although tremor is one of the most common movement disorders, there are few effective tremor-suppressing options available to patients. One potential tremor-suppression device involves a wearable gyrostabilizer similar to those used to stabilize cameras. However, we do not currently know how to design a gyrostabilizer to suppress tremor in an optimal manner. To address this gap, we present a systematic investigation of how gyrostabilizer parameters affect tremor suppression in a single degree of freedom (DOF). A simple model of the hand with a single DOF at the wrist and a gyroscope mounted on the back of the hand was used to focus on the most basic effects. After demonstrating that a linearized version of the non-linear equations of motion provides an adequate approximation, we simulated the frequency response of the system (hand + gyroscope) to a tremorogenic input torque at the wrist. By varying system parameters one at a time, we determined the effect of individual parameters on the frequency response of the system. To minimize the bandwidth without adding significant inertia about the wrist joint, the inertia and spin speed of the flywheel should be as high as design constraints allow, whereas the distance from the wrist joint axis to the gyroscope, the precession stiffness, and the precession damping should be kept as low as possible. The results demonstrate the potential of gyroscopic tremor suppression and can serve as the foundation for further investigations of gyroscopic tremor suppression in the upper limb.