We fit X-ray spectral data in the thermal dominant or high soft state of two dynamically confirmed black holes , GRO J1655-40 and 4U 1543-47 , and estimate the dimensionless spin parameters a _ { * } \equiv a / M of the two holes .
For GRO J1655-40 , using a spectral hardening factor computed for a non-LTE relativistic accretion disk , we estimate a _ { * } \sim 0.75 and \sim 0.65 - 0.75 , respectively , from ASCA and RXTE data .
For 4U 1543-47 , we estimate a _ { * } \sim 0.75 - 0.85 from RXTE data .
Thus , neither black hole has a spin approaching the theoretical maximum a _ { * } = 1 .