A vortex gyrating in a magnetic disk has two regimes of motion in the presence of disorder. At large gyration amplitudes, the vortex core moves quasi-freely through the disorder potential. As the amplitude decreases, the core can become pinned at a particular point in the potential and precess with a significantly increased frequency. In the pinned regime, the amplitude of the gyration decreases more rapidly than it does at larger precession amplitudes in the quasi-free regime. In part, this decreased decay time is due to an increase in the effective damping constant and in part due to geometric distortion of the vortex. A simple model with a single pinning potential illustrates these two contributions. ; Comment: 9 pages, 6 figures