Strong experimental indications exist that the top quark mass in the Standard Model (SM) exceeds the mass of the W gauge boson. Since this opens the decay mode t --> Wb a suitable regularization of the top quark propagator in the s-channel is required in many tree reactions. As in the Z(o) case this regularization essentially results in an additional imaginary contribution (i-GAMMA-(t)m(t)) to the propagator. This absorptive phase can combine with complex coupling constants of the charged current sector to give rise to new CP violating effects. Theoretical upper bounds for the size of these CP-odd signals are estimated in various extensions of the SM such as: the four generation SM, left-right symmetric models and models with two or three Higgs doublets.