The unusual flux variations of the pre-main-sequence binary star KH 15D have been attributed to occultations by a circumbinary disk. We test whether or not this theory is compatible with newly available data, including recent radial velocity measurements, CCD photometry over the past decade, and photographic photometry over the past 50 years. We find the model to be successful, after two refinements: a more realistic motion of the occulting feature and a halo around each star that probably represents scattering by the disk. The occulting feature is exceptionally sharp edged, raising the possibility that the dust in the disk has settled into a thin layer and providing a tool for fine-scale mapping of the immediate environment of a T Tauri star. However, the window of opportunity is closing, as the currently visible star may be hidden at all orbital phases by as early as 2008.