We studied the diffusion of 3D nanovoids in a bcc solid by kinetic Monte Carlo simulations. The diffusion coefficient as a function of the void size increases, reaches a maximum, and then decreases. The first increase is particularly interesting, as the diffusion of clusters is generally considered a decreasing function of the cluster size. We attribute this behavior to a curvature-dependent energy barrier for mass transport. We propose an analytical modeling of the void diffusion coefficient that reproduces the simulation data over the whole size range. In addition, for low temperatures and small sizes, the void diffusion coefficient vs size displays valleys, i.e., regions where the diffusion coefficient is smaller than the general trend. This behavior cannot be explained with analytical developments and is due to the formation of compact shapes for certain magic void sizes. In these shapes, the atoms at the void surface are strongly bound, displace less, and thus also void diffusion is slower.