We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for E/F a quadratic extension of p- adic fields the associated unitary group G = U(n, n + 1) contains a parabolic subgroup p with Levi component L isomorphic to GLn (E) X U1 (E). Let Π be an irreducible supercuspidal representation of L of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation lG P Π is reducible.