The effects of microstructure on the compressive properties of aggregated alumina suspensions are determined by intentionally introducing heterogeneities into the suspension. Suspensions are prepared at a high volume fraction and diluted with low hear hand mixing to a series of initial concentrations. As the initial concentration is increased, larger heterogeneities are introduced, and the suspension becomes more compressible relative to the compressive yield stress of the uniform suspension. A simple model is proposed in which the heterogeneous suspensions compress by rearrangement of the dense aggregates until a critical concentration (phi(c), which coincides with the volume fraction prior to dilution) is reached. Above phi(c), the suspensions consolidate identically to the uniform suspension. With a single fitting parameter (the size of the heterogeneities), the model shows semiquantitative agreement with the experimental data.