  We present evidence that the globular cluster NGC 6397 contains two distinct
classes of centrally-concentrated UV-bright stars. Color-magnitude diagrams
constructed from U, B, V, and I data obtained with the HST/WFPC2 reveal seven
UV-bright stars fainter than the main-sequence turnoff, three of which had
previously been identified as cataclysmic variables (CVs). Lightcurves of these
stars show the characteristic ``flicker'' of CVs, as well as longer-term
variability. A fourth star is identified as a CV candidate on the basis of its
variability and UV excess. Three additional UV-bright stars show no photometric
variability and have broad-band colors characteristic of B stars. These
non-flickering UV stars are too faint to be extended horizontal branch stars.
We suggest that they could be low-mass helium white dwarfs, formed when the
evolution of a red giant is interrupted, due either to Roche-lobe overflow onto
a binary companion, or to envelope ejection following a common-envelope phase
in a tidal-capture binary. Alternatively, they could be very-low-mass
core-He-burning stars. Both the CVs and the new class of faint UV stars are
strongly concentrated toward the cluster center, to the extent that mass
segregation from 2-body relaxation alone may be unable to explain their
distribution.
