ABSTRACT Emission-line velocity widths have been determined for 17 faint (B approximately 20-23) very blue, compact galaxies whose redshifts range from z = 0.095 to 0.66. The spectra have a resolution of 8 Km/s and were taken with the HIRES echelle spectrograph of the Keck 10 m telescope. The galaxies are luminous with all but two within 1 mag of M(sub B) approximately -21. Yet they exhibit narrow velocity widths between sigma = 28-157 km/s, more consistent with typical values of extreme star-forming galaxies than with those of nearby spiral galaxies of similar luminosity. In particular, objects with sigma is less than or equal to 65 km/s follow the same correlations between sigma and both blue and H beta luminosities as those of nearby H II galaxies. These results strengthen the identification of H II glaxies as thier local counterparts. The blue colors and strong emission lines suggest these compact galaxies are undergoing a recent, strong burst of star formation. Like those which characterize some H II galaxies, this burst could be a nuclear star-forming event within a much larger, older stellar population. If the burst is instead a major episode in the total star-forming history, these distant galaxies could fade enough to match the low luminosities and surface brightnesses typical of nearby spheroidals like NGC 185 or NGC 205. Together with evidence for recent star formation, exponential light profiles, and subsolar metallicities, the postfading correlations between luminosity and velocity width and bewtween luminosity and surface brightness suggest that among the low-sigma galaxies, we may be witnessing, in situ, the progenitors of today's spheroidal galaxies.