We consider new-physics (NP) contributions to the decay t → bbc. We parameterize the NP couplings by an effective Lagrangian consisting of 10 Lorentz structures. We show that the presence of NP can be detected through the measurement of the partial width. A partial identification of the NP can be achieved through the measurements of a forward-backward-like asymmetry, a topquark-spin-dependent asymmetry, the partial rate asymmetry, and a triple-product asymmetry.These observables, which vanish in the standard model, can all take values in the 10-20% range in the presence of NP. Since |V tb V cb | |V ts V cs |, most of our results also hold, with small changes, for