Previous searches for atomic gas in our Galaxy's dwarf spheroidal companions have not been sufficiently complete to settle the question of whether or not these galaxies have H I, especially in their outer parts. We present new observations of the dwarf spheroidals Sextans, Leo I, Ursa Minor, and Draco, using the NRAO 140 ft 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 H I column-density limits of 2-6x1017 cm-2. Unless H I is quite far from the galaxies' centers, we conclude that these galaxies do not contain significant amounts of atomic gas at the present time. We discuss whether the observations could have missed some atomic gas.