We present new observations of the Ly alpha lines of Epsilon Indi (K5 5) and A Andromedae (G8 4-3 ) These data were obtained by the Goddard High Resolution Spectrograph (GHRS) on the Hubble Space Telescope. Analysis of the interstellar H 1 and D 1 absorption lines reveals that the velocities and temperatures inferred from the H 1 lines are inconsistent with the parameters inferred from the D 1 lines, unless the H 1 absorption is assumed to be produced by two absorption components. One absorption component is produced by interstellar material. For both lines of sight observed, the velocity of this component is consistent with the velocity predicted by the local flow vector. For the Epsilon Indi data, the large velocity separation between the stellar emission and the interstellar absorption allows us to measure the H 1 column density independent of the shape of the intrinsic stellar Ly alpha profile. This approach permits us to quote an accurate column density and to assess its uncertainty with far more confidence than in previous analyses, for which the errors were dominated by uncertainties in the assumed stellar profiles.