  We investigate the direct and indirect bounds on dipole operators involving
the top quark. A careful analysis shows that the experimental upper limit on
the neutron electric dipole moment strongly constrains the chromo-electric
dipole of the top. We improve previous bounds by two orders of magnitude. This
has significant implications for new physics models and it also means that CP
violation in top pair production mediated by dipole operators will not be
accessible at the LHC. The CP conserving chromo-magnetic dipole moments are
constrained by recent measurements of the t\bar t spectrum by the ATLAS
collaboration. We also update the indirect constraints on electric and magnetic
dipole moments from radiative b -> s transitions, finding that they can be
considerably larger than their colored counterparts.
