A recently proposed two-stage flow/shrinkage model of leveling (or planarization) of uneven substrate topography during spin coating [Stillwagon and Larson, Phys. Fluids A 2, 1937 (1990)] is extended to account qualitatively for solvent evaporation. In the first, or flow, stage of the model, the film profile over a feature is assumed to be controlled by a balance of centrifugal and capillary forces within the lubrication approximation. This stage persists until solvent evaporation makes the film viscous enough that fluid rearrangement over a substrate feature is no longer possible. In the second, or shrinkage, stage, the film shrinks without flow by further evaporative drying. The transition between the two stages is assumed to occur abruptly at a polymer concentration φp1. This model is tested in spin coating studies with a series of polystyrene solutions spun on substrates with ideal trenchlike features, where the polymer molecular weight, the initial polymer concentration φp0, the spinning speed ω, the trench width w, and the radial distance r0 of the trench from the center of the substrate are varied. It is found that, except at low polymer concentrations, the model correctly predicts the dependence of the planarization on a dimensionless spinning speed proportional to ω2w3r0, and correctly predicts that φp1 is independent of spinning speed ω, but dependent on polymer concentration and on the ratio r0/w. The dependence of φp1 on initial polymer concentration and molecular weight correlates reasonably well with theoretical predictions, if a single fitting parameter is allowed.