The finite size of a gravitational microlens may have an effect on the observed amplification of a background point source. The mechanism is occlusion of one or more of the source images by the opaque bulk material of the lens as it travels in front of the source. To observe this phenomenon where both amplification and occlusion are important, the lensing geometry must be finely tuned so that the physical size of the lens is very near its Einstein radius. This condition makes the probability of an occlusion event extremely low; however, if such an event is detected, then the surface acceleration of the lens is constrained to within a geometrical factor related to the observer-lens distance. This information may provide a key to the identity of the lens. {copyright} {ital 1996 The American Astronomical Society.}