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We present photometry for three fields in the post-collapse globular cluster NGC 6624, using images obtained with the Faint Object Camera (FOC) on the Hubble Space Telescope (HST). We have developed an enhanced version of DAOPHOT that is better able to exploit the information contained in the first Airy ring around the core of the HST point-spread function. Color-magnitude diagrams reveal a well-defined red horizontal branch in the central and intermediate ($r = 28''$) fields, and at least ten candidate blue stragglers within five arcseconds of the cluster center. From the positions of individual stars in the crowded core, we determine the cluster center more accurately, and we present radial number density profiles of post-main-sequence stars; these profiles are suitable for comparison with Fokker-Planck models. In the outermost field ($r = 85''$), the main sequence is visible for three magnitudes below the turnoff.
