Ultraviolet spectra of intermediate resolution have been obtained with Copernicus for 12 objects classified as Be or shell stars and for 19 additional early B dwarfs. Some of these spectra show marked asymmetries in certain resonance lines, especially the Si IV doublet at 1400 A, indicating the presence in some cases of outflowing material with maximum velocities of nearly 1000 km/s. Direct evidence for mass loss at these velocities is seen for the first time in dwarf stars as late as B1.5; the only objects later than B0.5 which show this effect are Be or shell stars. Among the stars considered, there is a correlation between the presence of mass-loss effects and projected rotational velocity, suggesting that the ultraviolet flux from B1-B2 dwarfs is sufficient to drive high-velocity stellar winds only if rotational effects reduce the effective gravity near the equator. The mass-loss rate for one of the most active Be stars, 59 Cyg, is crudely estimated to be one billionth or one ten-billionth of a solar mass per year. The data suggest that the extended atmospheres associated with Be-star phenomena may be formed by mass ejection.