  The black-hole spin parameter, $a_*$, was measured to be close to its maximum
value of 1 in many accreting X-ray binaries. In particular, $a_*\gtrsim 0.9$
was found in a number of studies of LMC X-1. These measurements were claimed to
take into account both statistical and systematic uncertainties. We perform new
measurements using a recent simultaneous observation by NICER and NuSTAR,
providing a data set of high quality. We use the disk continuum method together
with improved models for coronal Comptonization. With the standard relativistic
disk model and optically thin Comptonization, we obtain values of $a_*$ similar
to those obtained before. We then consider modifications to the standard model.
Using a color correction of 2, we find $a_*\approx 0.64$--0.84. We then
consider disks with dissipation in surface layers. To account for that, we
assume the standard disk is covered by a warm and optically thick Comptonizing
layer. Our model with the lowest $\chi^2$ yields then $a_*\approx
0.40^{+0.41}_{-0.32}$. In order to test the presence of such effects in other
sources, we also study an X-ray observation of Cyg X-1 by Suzaku in the soft
state. We confirm the previous findings of $a_*>0.99$ using the standard model,
but then we find a weakly constrained $a_*\approx 0.82^{+0.16}_{-0.74}$ when
including an optically thick Comptonizing layer. We conclude that
determinations of the spin using the continuum method can be highly sensitive
to the assumptions about the disk structure.
