We study in detail the optimum technique for measuring lambda-21 cm absorption spectra with an aperture synthesis instrument. Using continuum sources behind galaxies in the Sculptor Group as examples, we derive formulae for the best estimate for the optical depth and the error on this estimate. In this case the dominant source of error is variation in the foreground H I emission of the disks of the galaxies, and we discuss how best to treat this problem. In addition to the absorption previously known toward the nucleus of NGC 253, new absorption is detected tentatively in one case in NGC 247. The H I gas in that case must be quite cool. The absorption in the nucleus of NGC 253 is of particular interest. We estimate the spin temperature by interpolating the emission spectra over the area of the continuum emission. The atomic gas temperature is extremely cold, below 25 K at some velocities. The H I seen in absorption is probably in the molecular clouds in the nuclear region.