  We present an empirical model of Comptonization for fitting the spectra of
X-ray binaries. This model, "simpl", has been developed as a package
implemented in XSPEC. With only two free parameters, simpl is competitive as
the simplest empirical model of Compton scattering. Unlike other empirical
models, such as the standard power-law model, simpl incorporates the basic
physics of Compton scattering of soft photons by energetic coronal electrons.
Using a simulated spectrum, we demonstrate that simpl closely matches the
behavior of physical Comptonization models which consider the effects of
optical depth, coronal electron temperature, and geometry. We present fits to
RXTE spectra of the black-hole transient H1743-322 and a BeppoSAX spectrum of
LMC X-3 using both simpl and the standard power-law model. A comparison of the
results shows that simpl gives equally good fits and a comparable spectral
index, while eliminating the troublesome divergence of the standard power-law
model at low energies. Importantly, simpl is completely flexible and can be
used self-consistently with any seed spectrum of photons. We show that simpl -
unlike the standard power law - teamed up with diskbb (the standard model of
disk accretion) gives results for the inner-disk radius that are unaffected by
strong Comptonization, a result of great importance for the determination of
black hole spin via the continuum-fitting method.
