The van der Waals interaction between perfectly spherical, infinitely hard spheres is well understood. Unfortunately, real powder particles are not infinitely hard and rarely spherical. Those particles that are approximately spherical are often covered in small asperities. It is often believed that the size of these asperities dominates the cohesive force between powder particles, This paper rigorously examines this phenomenon and demonstrates the regimes over which the asperities dominate the cohesive force and when the particle size dominates. Deformation of particles is also investigated with a simple model and is shown to produce a significant increase in cohesive force. We demonstrate that previous simple models for calculating the effect of deformation are inadequate, as they ignore effects that can be as large as the correction they suggest. This can lead to an underestimation of the cohesive force by a factor of approximately 2.