We show that it is possible to accommodate the observed size of the phase in B-s(0) - (B) over bar (0)(s) mixing in the framework of a model with violation of 3 x 3 unitarity. This violation is associated to the presence of a new Q = 2/3 isosinglet quark T, which mixes both with t and c and has a mass not exceeding 500 GeV. The crucial point is the fact that this framework allows for chi equivalent to arg(-VtsVcbVtb*V-cs*) of order lambda, to be contrasted with the situation in the standard model, where chi is constrained to be of order lambda(2). We point out that this scenario implies rare top decays t -> cZ at a rate observable at the LHC and vertical bar V-tb vertical bar significantly different from unity. In this framework, one may also account for the observed size of D-0 - (D) over bar (0) mixing without having to invoke long-distance contributions. It is also shown that in the present scenario, the observed size of D-0 - (D) over bar (0) mixing constrains chi' equivalent to arg(-VcdVusVcs*V-ud*) to be of order lambda(4), which is significantly smaller than what is allowed in generic models with violations of 3 x 3 unitarity.