to severe crowding, we ran three DAOPHOT II detection passes to identify and measure faint stars and to improve the photometry for the bright stars. After each pass, we subtracted all detected stars from the images and reran the finding algorithm to search for any newly-revealed faint stars. Three such passes yielded a candidate list of roughly 24,000 objects. Passing this list on to ALLFRAME resulted in the elimination of $\approx 4000$ objects, leaving a total of 19,969 measured stars. The final CM diagram is approximately one magnitude deeper at the 50% completeness level than it had been using a single detection pass.

Identical procedures were used to find and measure stars in the POS2 field, yielding a total of 4111 stars. Under ideal conditions, correcting for M31 background stars in the M32 field would require that, for each star found in POS2, we subtract from the POS1 sample the star most similar in color and magnitude. However, image crowding is clearly more important for POS1 than POS2, and proper accounting needs to be taken of their differing levels of completeness. Moreover, owing to a miscalculation, the POS2 field as observed lies about 57” outwards from the M31 isophote that 