Abstract: A gyroscopic roll stabilizer for a boat. The stabilizer includes a flywheel, a flywheel drive motor configured to spin the flywheel about a spin axis, an enclosure surrounding a portion or all of the flywheel and maintaining a below-ambient pressure or containing a below-ambient density gas, a gimbal structure configured to permit flywheel precession about a gimbal axis, and a device for applying a torque to the flywheel about the gimbal axis. The flywheel, enclosure, and gimbal structure are configured so that when installed in the boat the stabilizer damps roll motion of the boat. Preferably, the flywheel drive motor spins the flywheel at high tip speeds.