  We measure the spin of XTE J1550-564 in two ways: by modelling the thermal
continuum spectrum of the accretion disc, and independently by modeling the
broad red wing of the reflection fluorescence Fe-K line. We find that the spin
measurements conducted independently using both leading methods are in
agreement with one another. For the continuum-fitting analysis, we use a data
sample consisting of several dozen RXTE spectra, and for the Fe-K analysis, we
use a pair of ASCA spectra from a single epoch. Our spin estimate for the black
hole primary using the continuum-fitting method is -0.11 < a* < 0.71 (90 per
cent confidence), with a most likely spin of a* = 0.34. In obtaining this
result, we have thoroughly explored the dependence of the spin value on a wide
range of model-dependent systematic errors and observational errors; our
precision is limited by uncertainties in the distance and orbital inclination
of the system. For the Fe-line method, our estimate of spin is a* =
0.55(+0.15,-0.22). Combining these results, we conclude that the spin of this
black hole is moderate, a* = 0.49(+0.13,-0.20), which suggests that the jet of
this microquasar is powered largely by its accretion disc rather than by the
spin energy of the black hole.
