The transient behavior of the viscosity (stress growth) of a weakly aggregating polystyrene latex dispersion after a step from a high shear rate to a lower shear rate has been measured and modeled. Single particles cluster together into spherical fractal aggregates. The steady state size of these aggregates is determined by the shear stresses exerted on the latter by the flow field. The restructuring process taking place when going from a starting situation with monodisperse spherical aggregates to larger monodisperse spherical aggregates is described by the capture of primary fractal aggregates by growing aggregates until a new steady state is reached. It is assumed that the aggregation mechanism is diffusion limited. The model is valid if the radii of primary aggregates R(prim). are much smaller than the radii of the growing aggregates. Fitting the model to experimental data at two volume fractions and a number of step sizes in shear rate yielded physically reasonable values of R(prim) at fractal dimensions 2.1 less-than-or-equal-to d(f) less-than-or-equal-to 2.2. The latter range is in good agreement with the range 2.0 less-than-or-equal-to d(f) less-than-or-equal-to 2.3 obtained from steady shear results. The experimental data have also been fitted to a numerical solution of the diffusion equation for primary aggregates for a cell model with moving boundary, also yielding 2.1 less-than-or-equal-to d(f) less-than-or-equal-to 2.2. The range for d(f) found from both approaches agrees well with the range d(f) almost-equal-to 2.1-2.2 determined from computer simulations on diffusion-limited aggregation including restructuring or thermal breakup after formation of bonds. Thus a simple model has been put forward which may capture the basic features of the aggregating model dispersion on a microstructural level and leads to physically acceptable parameter values.