  We collect new and archival optical observations of nine "black-widow"
millisecond pulsar binaries. New measurements include direct imaging with the
Keck, Gemini-S, MDM, and LCO 2~m telescopes. This is supplemented by
synthesized colors from Keck long-slit spectra. Four black-widow optical
companions are presented here for the first time. Together these data provide
multicolor photometry covering a large fraction of the orbital phase. We fit
these light curves with a direct (photon) heating model using a version of the
ICARUS light-curve modeling code. The fits provide distance and fill-factor
estimates, inclinations, and heating powers. We compare the heating powers with
the observed GeV luminosities, noting that the ratio is sensitive to pulsar
distance and to the gamma-ray beaming. We make a specific correction for
"outer-gap" model beams, but even then some sources are substantially
discrepant, suggesting imperfect beaming corrections and/or errors in the fit
distance. The fits prefer large metal abundance for half of the targets, a
reasonable result for these wind-stripped secondaries. The companion radii
indicate substantial Roche-lobe filling, $f_c \approx 0.7-1$ except for PSR
J0952$-$0607, which with $f_c< 0.5$ has a companion density $\rho \approx
10\,{\rm g\,cm^{-3}}$, suggesting unusual evolution. We note that the
direct-heating fits imply large heating powers and rather small inclinations,
and we speculate that unmodeled effects can introduce such bias.

High Energy Astrophysical Phenomena