Absorption at the Lyman-α transition from interstellar neutral hydrogen has been observed in the ultraviolet spectra of 18 nearby O and B stars. Radiation damping is the dominant cause of line broadening, which makes the derived line-of-sight column densities proportional to the square of the observed equivalent widths. An average hydrogen density on the order of 0.1 atom cm−3 has been found for most of the stars observed so far. This is in contrast to the findings from surveys of 21-cm radio emission, which suggest 0.7 atom cm−3 exists in the local region of the Galaxy. Several effects which might introduce uncertainties into the Lyman-α measurements are considered, but none seems to be able to produce enough error to explain the disagreement with the 21-cm data. The possibility that small-scale irregularities in the interstellar gas could give significantly lower values at Lyman-α is explored. However, a quantitative treatment of the factor of ten discrepancy in Orion indicates the only reasonable explanation requires the 21-cm flux to come primarily from small, dense, hot clouds which are well separated from each other. The existence of such clouds, however, poses serious theoretical difficulties.