The effect of annealing on the structure of the surface of single crystals of ice crushed at 77.15 K is investigated using methane adsorption at 77.15 and 87.1 K. Methane adsorption isotherms are obtained for surface coverages, theta, between 0.1 and 1.5 monolayers and between 10(-6) and 10(-2) monolayer. It is observed that annealing greatly reduces the number of CH4 molecules adsorbed at low coverage (by a factor of 10 at P-CH4 = 10(-4) Torr, for annealing at 238 K), but no effect of annealing on adsorption is observed for theta greater than 0.1 monolayer. We propose that these effects are due to the disappearance upon annealing of crystal faces with favorable adsorption sites, which could be faces with high Miller-Bravais indices. From our data, and additional data obtained by other investigators, we conclude that the mode of formation and the thermal history of the ice surface strongly influence its surface structure and adsorption properties. We discuss the possibility that the different modes of formation of ice in the atmosphere will result in different surface and adsorption properties.