The thermal dependence of the lamellar thickness (L-p) and the thickness of crystalline layers of linear polyethylene single crystals has been revisited. LPE fractions with different average molecular weights were crystallized at the same temperatures to avoid the delicate problem of an arbitrary choice of their equilibrium dissolution temperature to calculate their degree of supercooling. This procedure allows direct check of the thicknesses of the crystalline layers dependence on the degree of supercooling. Indeed, the equilibrium melting and dissolution temperatures depend on the average molecular weight. Mats of linear polyethylene single crystals of various narrow molecular weight fractions were obtained from dilute p-xylene solutions. Their lamellar thickness was determined from the SAXS intensity curve. The crystalline layers thickness was calculated from the linear correlation function of the SAXS intensity curves and from the LAM mode frequency of the Raman spectrum. It depends as expected on the crystallization temperature. However, at a given crystallization temperature, both the thicknesses of the lamellae and of the crystalline layers are nearly independent of molecular weight and therefore also of the degree of supercooling estimated from a well-known semiempirical relationship.