  We present simultaneous Chandra-HETG and RXTE observations of a moderate flux
`soft state' of the black hole candidate 4U1957+11. These spectra, having a
minimally discernible hard X-ray excess, are an excellent test of modern disk
atmosphere models that include the effects of black hole spin. The HETG data
show that the soft disk spectrum is only very mildly absorbed with N_H =1-2 X
10^{21} cm^-2. These data additionally reveal 13.449 A NeIX absorption
consistent with the warm/hot phase of the interstellar medium. The fitted disk
model implies a highly inclined disk around a low mass black hole rapidly
rotating with normalized spin a*~1. We show, however, that pure Schwarzschild
black hole models describe the data extremely well, albeit with large disk
atmosphere ``color-correction'' factors. Standard color-correction factors can
be attained if one additionally incorporates mild Comptonization. We find that
the Chandra observations do not uniquely determine spin. Similarly, XMM/RXTE
observations, taken only six weeks later, are equally unconstraining. This lack
of constraint is partly driven by the unknown mass and unknown distance of
4U1957+11; however, it is also driven by the limited bandpass of Chandra and
XMM. We therefore present a series of 48 RXTE observations taken over the span
of several years and at different brightness/hardness levels. These data prefer
a spin of a*~1, even when including a mild Comptonization component; however,
they also show evolution of the disk atmosphere color-correction factors. If
the rapid spin models with standard atmosphere color-correction factors of
h_d=1.7 are to be believed, then the RXTE observations predict that 4U1957+11
can range from a 3 M_sun black hole at 10 kpc with a*~0.83 to a 16 M_sun black
hole at 22 kpc with a* ~ 1, with the latter being statistically preferred.
