The present invention is directed to a composition and process for shaving a surface, such as human skin having hair projecting therefrom. The process involves the steps of: (a) providing a surface to be shaved; (b) providing a composition containing: (i) at least one non-aqueous polar organic compound having at least two hydroxyl groups; (ii) optionally, at least one emollient; (iii) optionally, at least one thickening agent; (iv) optionally, at least one fragrance; and (v) optionally, water; (c) optionally, wetting the surface to be shaved; (d) applying the composition onto the surface to be shaved in order to form a treated surface; and (e) shaving the treated surface.