  We have chosen 6 Ultra-Luminous X-ray sources from the {\it XMM-Newton}
archive whose spectra have high signal-to-noise and can be fitted solely with a
disk model without requiring any power-law component. To estimate systematic
errors in the inferred parameters, we fit every spectrum to two different disk
models, one based on local blackbody emission (KERRBB) and one based on
detailed atmosphere modelling (BHSPEC). Both incorporate full general
relativistic treatment of the disk surface brightness profile, photon Doppler
shifts, and photon trajectories. We found in every case that they give almost
identical fits and similar acceptable parameters. The best-fit value of the
most interesting parameter, the mass of the central object, is between 23 and
73 M$_\sun$ in 5 of the 6 examples. In every case, the best-fit inclination
angle and mass are correlated, in the sense that large mass corresponds to high
inclination. Even after allowing for this degeneracy, we find that, with
$\gtrsim 99.9%$ formal statistical confidence, 3 of the 6 objects have mass
$\gtrsim 25 M_\sun$; for the other 3, these data are consistent with a wide
range of masses. A mass greater than several hundred $M_\sun$ is unlikely for
the 3 best-constrained objects. These fits also suggest comparatively rapid
black hole spin in the 3 objects whose masses are relatively well-determined,
but our estimate of the spin is subject to significant systematic error having
to do with uncertainty in the underlying surface brightness profile.
