  We predict the level of small-scale anisotropy in the cosmic microwave
background (CMB) due to the Sunyaev--Zel'dovich (SZ) effect for the ensemble of
cosmological models that are consistent with current measurements of
large-scale CMB anisotropy. We argue that the recently reported detections of
the small-scale (arcminutes) CMB anisotropy are only marginally consistent with
being the SZ effect when cosmological models are calibrated to the existing
primary CMB data on large scales. The discrepancy is at more than 2-2.5 sigma,
and is mainly due to a lower sigma_8 <0.8 favored by the primary CMB and a
higher sigma_8 > 1 favored by the SZ effect. A degeneracy between the optical
depth to Thomson scattering and the CMB-derived value of sigma_8 suggests that
the discrepancy is reduced if the universe was reionized very early, at a
redshift of about 25.
