The effect of microstructure on the rheology of clay/polymer nanocomposites is investigated using dispersions of organically treated clay in nearly Newtonian poly(dimethylsiloxane). Degree of dispersion and floc size are altered by using two different dispersion procedures and by changing the shear history. The scaling for dynamic moduli of attractive colloids applies, except for a possible relaxation mechanism at very low frequencies. The time to reach the crossover at a given frequency is found to be extremely sensitive to the dispersion procedure used. Hydrodynamic and elastic components of the steady state stress, on the other hand, evolve in a very similar fashion for the different systems. Although the relaxation times of the elastic stress components change drastically with flow-induced changes in structure, the dispersion process hardly has an effect at all. Intermittent start-up flows in the forward and reverse directions show that anisotropy persists long after the flow has been arrested, even at shear rates where no large reversible flocs are present. The degree of dispersion only had a limited effect on the anisotropy. Finally, the effect of shear on structure recovery has been studied. Very low shear rates are found to increase the rate of recovery, even for small strains.