We present results from spectral modeling of three black hole X-ray binaries : LMC X-3 , GRO J1655-40 , and XTE J1550-564 . Using a sample of disk dominated observations , we fit the data with a range of spectral models that includes a simple multitemperature blackbody ( DISKBB ) , a relativistic accretion disk model based on color-corrected blackbodies ( KERRBB ) , and a relativistic model based on non-LTE atmosphere models within an \alpha prescription ( BHSPEC ) . BHSPEC provides the best fit for a BeppoSAX observation of LMC X-3 , which has the broadest energy coverage of our sample . It also provides the best fit for multiple epochs of Rossi X-ray Timing Explorer ( RXTE ) data in this source , except at the very highest luminosity ( L / L _ { Edd } \gtrsim 0.7 ) , where additional physics must be coming into play . BHSPEC is also the best-fit model for multi-epoch RXTE observations of GRO J1655-40 and XTE J1550-564 , although the best-fit inclination of the inner disk differs from the binary inclination . All our fits prefer \alpha = 0.01 to \alpha = 0.1 , in apparent disagreement with the large stresses inferred from the rapid rise times observed in outbursts of these two sources . In all three sources our fits imply moderate black hole spins ( a _ { \ast } \sim 0.1 - 0.8 ) , but this is sensitive to the reliability of independent measurements of these system parameters and to the physical assumptions which underly our spectral models .