In the production of polyethylene foams by extrusion with alkanes as a blowing agent, significant changes in the dimensions of extruded products are encountered. The dimensional stability of a foam with a structure of closed cells is improved by blending the polymer with small amounts of a low molecular weight additive. It is believed that the dimensional stability is related to the ratio of the blowing agent to air permeability. It is shown in this article that the additive reduces the blowing agent permeability more than it does the air permeability only if the additive has migrated to the surface of the polymer. The presence of the additive at the polymer surface has been confirmed by electron microscopy and infrared spectroscopy. The (partially) ordening of the additive at the surface, as shown with wide-angle X-ray diffraction, explains the low gas permeabilities of the additive compared to the corresponding permeabilities of polyethylene.