In R p -violating supersymmetric theories there are new two-body top quark decays which can substantially suppress the branching fraction of the Standard Model process t → bW+ → bℓ+ν ℓ . With some choices of the dominant R p -violating operator theCDF top-quark mass bound can be lowered below the LEP bound. With other choices, however, leptonic signals from top decay become much stronger; in such scenarios the bounds on the top-quark mass become more stringent than the Standard Model bounds. In future top-quark searches R p -violating decays could lead to the most prominent signals.