  We present the results of an all-sky, deep optical survey for faint Local
Group dwarf galaxies. Candidate objects were selected from the second Palomar
survey (POSS-II) and ESO/SRC survey plates and follow-up observations performed
to determine whether they were indeed overlooked members of the Local Group.
Only two galaxies (Antlia and Cetus) were discovered this way out of 206
candidates. Based on internal and external comparisons, we estimate that our
visual survey is more than 77% complete for objects larger than one arc minute
in size and with a surface brightness greater than an extremely faint limit
over the 72% of the sky not obstructed by the Milky Way. Our limit of
sensitivity cannot be calculated exactly, but is certainly fainter than 25
magnitudes per square arc second in R, probably 25.5 and possibly approaching
26. We conclude that there are at most one or two Local Group dwarf galaxies
fitting our observational criteria still undiscovered in the clear part of the
sky, and a roughly a dozen hidden behind the Milky Way. Our work places the
"missing satellite problem" on a firm quantitative observational basis. We
present detailed data on all our candidates, including surface brightness
measurements.
