We present new upper limits on the neutral hydrogen ( H i ) content within the stellar half-light ellipses of 15 Galactic dwarf spheroidal galaxies ( dSphs ) , derived from pointed observations with the Green Bank Telescope ( GBT ) as well as Arecibo L-band Fast ALFA ( ALFALFA ) survey and Galactic All-Sky Survey ( GASS ) data . All of the limits M _ { HI } ^ { lim } are more stringent than previously reported values , and those from the GBT improve upon contraints in the literature by a median factor of 23 . Normalizing by V -band luminosity L _ { V } and dynamical mass M _ { dyn } , we find M _ { HI } ^ { lim } / L _ { V } \sim 10 ^ { -3 } \mathrm { M _ { \odot } / L _ { \odot } } and M _ { HI } ^ { lim } / M _ { dyn } \sim 5 \times 10 ^ { -5 } , irrespective of location in the Galactic halo . Comparing these relative H i contents to those of the Local Group and nearby neighbor dwarfs compiled by McConnachie , we find that the Galactic dSphs are extremely gas-poor . Our H i upper limits therefore provide the clearest picture yet of the environmental dependence of the H i content in Local Volume dwarfs . If ram pressure stripping explains the dearth of H i in these systems , then orbits in a relatively massive Milky Way are favored for the outer halo dSph Leo I , while Leo II and Canes Venatici I have had a pericentric passage in the past . For Draco and Ursa Minor , the interstellar medium mass that should accumulate through stellar mass loss in between pericentric passages exceeds M _ { HI } ^ { lim } by a factor of \sim 30 . In Ursa Minor , this implies that either this material is not in the atomic phase , or that another mechanism clears the recycled gas on shorter timescales .