Quantitative analyses of the isothermal desorption kinetics from methanol-doped H2O films on Pt( 111) reveal that transport kinetics for CH3OH in polycrystalline ice are much slower than previously reported. They also indicate that MeOH displays first-order desorption kinetics with respect to its instantaneous surface concentration below 0.1 mole fraction in ice. These observations allow isothermal desorption rate measurements to be interpreted in terms of a depth profiling analysis providing one-dimensional concentration depth profiles from methanol-doped polycrystalline ice films. Using a straightforward approach to inhibit ice sublimation, transport properties are extracted from the evolution of concentration depth profiles obtained after thermal annealing of binary ice films at high temperature. Heterodiffusion coefficients for methanol in polycrystalline ( cubic) ice I-c films are reported for temperatures between 145 and 195 K and for concentrations below 10(-3) mole fraction. Finally, diffusion kinetics for methanol in ice are shown to display a very strong concentration dependence that may contribute, in addition to variations in laboratory samples microstructure, to the disagreements reported in the literature regarding the transport properties of ice.