Aqueous dispersions of latex particles have been aggregated by addition of Ca2+ ions and then filtered in a pressure filtration cell. The filtration cakes have been examined through small-angle neutron scattering, void volume fraction measurements, and permeate flux measurements. At all filtration pressures (20-400 kPa), the cakes were extensively collapsed (latex volume fractions phi = 0.27-0.46), and the remaining porosity had a tenuous structure (fractal dimensions d(f) = 1.3-1). However, the local structures remained the same as in the aggregates of the original suspensions. The mechanisms that produce this collapse are made of very small relative motions of the particles, which leave the local coordination of the latex particles unchanged but allow large voids to be reduced. These motions could be inhibited by using particles with nonspherical shapes and by increasing the friction forces that act between particle surfaces, thereby reducing the extent of collapse and increasing the permeability of the cakes.