We report results of simulations of a model for concentrated aggregated colloidal dispersions under shear flows. In an effort to study trends in rheology for varying colloidal interactions, we study a reduced hydrodynamic, frame-invariant, pair-drag model in which a long-range, many-body mobility matrix is generated just from resistance pair-drag terms that include lubrication. The model also includes depletion interactions, repulsive surface forces, and Brownian forces. We consider the steady-state rheology of the model which we varied in volume fraction between 30% and 53%. We are able to fit our data to experimental results. The rheology of the model is that of a power-law shear-thinning fluid with relative viscosity scaling with shear rate as nr ~y-a 2a and an exponent close to universal over a range of particle volume fractions 0.45–0.53. We also obtained a shear-thinning exponent that appears to be just weakly sensitive to the hydrodynamic model. The exponent a varies from 0.7560.02 for weakly aggregating systems to 0.8660.03 in the case of strong aggregating systems and the experimental data. As we lower the volume fraction we find a model-dependent transition to shear banding, where the rheology is effectively lost. We also find evidence of transitions between different shear-thinning regimes at the higher volume fractions when the particles are arranged in the familiar strings phases.