We have observed four lunar occultations of the Galactic center in the infrared K band, three with infrared cameras and one by high-speed photometry. The occultation observations enable us to estimate the sizes of objects brighter than K ∼ 10 mag in the central parsec of the Galaxy, and, for objects brighter than K ∼ 11, to separate them from their surroundings and to measure their fluxes. Of the relatively bright K-band sources within 3″ of Sgr A*, IRS 16NE, 16NW, and 29 are smaller than ∼510 AU, and IRS 16C and a compact component of IRS 16SW are smaller than 85 AU. They are probably stars. About half the flux from this central 3″ radius region is diffuse emission that is probably contributed by an unresolved cluster of stars. There is no peak of K-band emission at Sgr A* to a limit of about 10.6 mag. IRS 1W and 13 are resolved into pairs of sources; they are probably the stars that excite these H n regions. IRS 7 is smaller than 100 AU. It has a faint companion. The shape of the luminosity functions for the central pc2 and the central ∼150 pc2 (Lebofsky and Rieke) are similar.