The transformation of an atomic nucleus into two excited fission fragments is modeled as a strongly damped evolution of the nuclear shape. As in previous studies, it is assumed that the division of mass and charge is frozen in at a critical neck radius of c0=2.5fm. In order to also determine the energetics, we follow the system further until scission occurs at a smaller neck radius, at which point the shapes of the proto-fragments are extracted. The statistical energy available at scission is then divided on the basis of the respective microscopic level densities. This approach takes account of important (and energy-dependent) finite-size effects. After the fragments have been fully accelerated and their shapes have relaxed to their equilibrium forms, they undergo sequential neutron evaporation. The dependence of the resulting mean neutron multiplicity on the fragment mass, ν¯(A), including the dependence on the initial excitation energy of the fissioning compound nucleus, agrees reasonably well with observations, as demonstrated here for 235U(n,f), and the sawtooth appearance of ν¯(A) can be understood from shell-structure effects in the level densities. Keywords: Fission, Brownian shape evolution method, Microscopic level densities