Possible anomalous couplings of the top quark to on-shell photons and
gluons are constrained by the recent results of the CLEO Collaboration
on both inclusive and exclusive radiative B decays. We find that the
process b --> sgamma can lead to reasonable bounds (of order a few X 1
0(16) e cm) on both the anomalous electric and magnetic dipole moments
of the top quark. Essentially no limits are obtained on the correspon
ding chromoelectric and chromomagnetic moments, which enter the expres
sion for the decay rate only through operator mixing.