The spectral evolution of a passive scalar experiencing steady stirring imposed by a narrow-band velocity spectrum is examined. An extra term is included in the scalar spectrum equation in order to represent the non-local, direct transfer put forward by Kerstein and McMurtry (Phys. Rev. E, 50 (1994) 2057). It is found that, at large times, this mechanism drives the scalar spectrum to develop the scaling predicted by the latter authors with, however, a significantly faster decay. Furthermore, under these conditions, the computed growth of the scalar lengthscales is superdiffusive.