  All prior work on measuring the spins of stellar-mass black holes via the
X-ray continuum-fitting method has relied on the use of weakly-Comptonized
spectra obtained in the thermal dominant state. Using a self-consistent
Comptonization model, we show that one can analyze spectra that exhibit strong
power-law components and obtain values of the inner disk radius, and hence
spin, that are consistent with those obtained in the thermal dominant state.
Specifically, we analyze many RXTE spectra of two black hole transients,
H1743-322 and XTE J1550-564, and we demonstrate that the radius of the inner
edge of the accretion disk remains constant to within a few percent as the
strength of the Comptonized component increases by an order of magnitude, i.e.,
as the fraction of the thermal seed photons that are scattered approaches 25%.
We conclude that the continuum-fitting method can be applied to a much wider
body of data than previously thought possible, and to sources that have never
been observed to enter the thermal dominant state (e.g., Cyg X-1).
