  Continuum and reflection spectral models have each been widely employed in
measuring the spins of accreting black holes. However, the two approaches have
not been implemented together in a photon-conserving, self-consistent
framework. We develop such a framework using the black-hole X-ray binary GX
339-4 as a touchstone source, and we demonstrate three important ramifications:
(1) Compton scattering of reflection emission in the corona is routinely
ignored, but is an essential consideration given that reflection is linked to
the regimes with strongest Comptonization. Properly accounting for this causes
the inferred reflection fraction to increase substantially, especially for the
hard state. Another important impact of the Comptonization of reflection
emission by the corona is the downscattered tail. Downscattering has the
potential to mimic the relativistically-broadened red wing of the Fe line
associated with a spinning black hole. (2) Recent evidence for a reflection
component with a harder spectral index than the power-law continuum is
naturally explained as Compton-scattered reflection emission. (3) Photon
conservation provides an important constraint on the hard state's accretion
rate. For bright hard states, we show that disk truncation to large scales (R
much larger than the ISCO radius) is unlikely as this would require accretion
rates far in excess of the brightest soft states. Our principal conclusion is
that when modeling relativistically-broadened reflection, spectral models
should allow for coronal Compton scattering of the reflection features, and
when possible, take advantage of the additional constraining power from linking
to the thermal disk component.
