Two limiting regimes of small molecule diffusion in polymers are widely acknowledged: Fickian and case II. Case II diffusion is associated with solvent uptake proceeding linearly with time. Linear uptake is normally described by models that assume the viscoelastic polymer swelling at the solvent front to be the rate-limiting step in the transport process. In this paper we observe that, so long as a solvent-driven glass to rubber transition exists, the rate-limiting step can alternately be the solvent flux at the polymer surface. The case II velocity then depends on the surface flux. Varying this flux can vary the case II front velocity in a manner not explicable using established models. It can also drive a transition between Fickian and case II transport. An additional outcome is that varying the solvent flux permits a new method of accessing any concentration history dependence of the solvent diffusivity in the polymer. Numerical simulations of a simple phenomenological model illustrating Fickian diffusion, conventional solvent-front-limited case II diffusion, and surface-flux-limited case II diffusion are presented. The modeling is supported by experimental measurements of liquid and vapor toluene ingress into polystyrene using magnetic resonance imaging (MRI) and stray field imaging (STRAFI). Vapor flux and temperature are varied.