Thin polymer films have striking dynamical properties that differ from their bulk counterparts. With the simple geometry of a stepped polymer film on a substrate, we probe mobility above and below the glass transition temperature T-g. Above T-g the entire film flows, whereas below T-g only the near-surface region responds to the excess interfacial energy. An analytical thin-film model for flow limited to the free surface region shows excellent agreement with sub-T-g data. The system transitions from whole-film flow to surface localized flow over a narrow temperature region near the bulk T-g. The experiments and model provide a measure of surface mobility in a simple geometry where confinement and substrate effects are negligible. This fine control of the glassy rheology is of key interest to nanolithography among numerous other applications.