We consider new-physics (NP) contributions to the decay t→bb̄c. We parametrize 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 top-quark-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 tbVcb|VtsVcs|, most of our results also hold, with small changes, for t→ss̄c.