  Previous searches for atomic gas in our Galaxy's dwarf spheroidal companions
have not been complete enough to settle the question of whether or not these
galaxies have HI, especially in their outer parts. We present new observations
of the dwarf spheroidals Sextans, Leo I, Ursa Minor, and Draco, using the NRAO
140-foot telescope to search much farther in radius than has been done before.
The new data go out to at least 2.5 times the core radius in all cases, and
well beyond even the tidal radius in two cases. These observations give HI
column density limits of 2-6 x 10^17 atoms cm^-2. Unless HI is quite far from
the galaxies' centers, we conclude that these galaxies don't contain
significant amounts of atomic gas at the present time. We discuss whether the
observations could have missed some atomic gas.
