  Light curves, explosion energies, and remnant masses are calculated for a
grid of supernovae resulting from massive helium stars that have been evolved
including mass loss. These presupernova stars should approximate the results of
binary evolution for stars in interacting systems that lose their envelopes
close to the time of helium core ignition. Initial helium star masses are in
the range 2.5 to 40\,\Msun, which correspond to main sequence masses of about
13 to 90\,\Msun. Common Type Ib and Ic supernovae result from stars whose final
masses are approximately 2.5 to 5.6\,\Msun. For heavier stars, a large fraction
of collapses lead to black holes, though there is an island of explodability
for presupernova masses near 10\,\Msun. The median neutron star mass in
binaries is 1.35--1.38\,\Msun \ and the median black hole mass is between 9 and
11\,\Msun. Even though black holes less massive than 5 \Msun\ are rare, they
are predicted down to the maximum neutron star mass. There is no empty ``gap'',
only a less populated mass range. For standard assumptions regarding the
explosions and nucleosynthesis, the models predict light curves that are
fainter than the brighter common Type Ib and Ic supernovae. Even with a very
liberal, but physically plausible increase in $^{56}$Ni production, the highest
energy models are fainter, at peak, than 10$^{42.6}$\,erg\,s$^{-1}$, and very
few approach that limit. The median peak luminosity ranges from 10$^{42.0}$ to
10$^{42.3}$\,erg\,s$^{-1}$. Possible alternatives to the standard
neutrino-powered and radioactive-illuminated models are explored. Magnetars are
a promising alternative. Several other unusual varieties of Type I supernovae
at both high and low mass are explored.
