  We analyze local ISM absorption observed in the Lyman-alpha and Mg II h & k
lines of six nearby K dwarf stars, using UV spectra of these stars obtained
with the Goddard High Resolution Spectrograph on the Hubble Space Telescope.
For four of the six stars, we detect an absorption component with a velocity
and column density consistent with the Local Interstellar Cloud (LIC). For HD
197890, there is no observed component at the expected LIC velocity, or at the
projected velocity of the G cloud, which is a nearby cloud in the general
direction of the Galactic Center. It also seems doubtful that either of the two
components seen toward HD 82558 are LIC or G cloud absorption. The total H I
column density toward HD 82558 (d=18.3 pc) is extremely high (log N(H)=19.05
+/- 0.15), representing the largest average H I density detected for any line
of sight through the nearby LISM (n(H)=0.2 cm^-3). This is particularly
remarkable considering that this star is only 39 degrees from the "interstellar
tunnel" toward Epsilon CMa, where column densities are an order of magnitude
lower than this toward stars which are an order of magnitude farther away.
