  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* = 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* ~ 0.75 and ~ 0.65-0.75, respectively, from ASCA and RXTE
data. For 4U 1543-47, we estimate a* ~ 0.75-0.85 from RXTE data. Thus, neither
black hole has a spin approaching the theoretical maximum a* = 1.
