Collision efficiencies are considered for colloidal suspensions of solid spheres moving in a viscous fluid under the influence of electrophoresis or gravity, Brownian motion, and electrostatic and van der Waals forces. The results are compared to those for convection (electrophoresis or gravity) and diffusion (Brownian motion) acting independently. The collision efficiency increases by many orders of magnitude over that predicted by simply adding diffusive and convective efficiencies in a specific parameter regime, This regime occurs when there is a large energy barrier in the inter-particle potential, causing a stable region of parameter space if there is no diffusion. Brownian motion alone will only cause small amounts of aggregation under these conditions. However, for electric fields or buoyancy effects which are only slightly too weak to allow particles to overcome the potential barrier, the addition of weak Brownian motion to a system with convection can cause significant numbers of particles to overcome the energy barrier and aggregate.