Previous searches for H I in our Galaxy's dwarf spheroidal companions have not been complete enough to settle the question of whether or not these galaxies have H I, especially in their outer parts. We present VLA observations of three dwarf spheroidals: Fornax, Leo II, and Draco, all of which have known stellar velocities. The new data show no H I emission or absorption. Column density limits in emission are 4 × 1018 to 7 × 1018 cm-2 in the centers of the galaxies. The importance of the new observations is that they cover larger areas than previous searches and are less plagued by confusion with foreground (Galactic) H I. The apparent absence of neutral gas in the Fornax dwarf spheroidal is especially puzzling, because recent photometry shows evidence of stars only 108 years old. We discuss whether the VLA observations could have missed significant amounts of H I.
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