The low-strain mechanical properties of linear polyethylene (PE) can be substantially altered by the incorporation of a short block of a polymer with a high glass transition temperature (T-g) into a majority-PE block copolymer. In particular, the yield stress and the tensile modulus can be sharply increased with the addition of a relatively small fraction of glassy block, especially when combined with a thermal history that promotes high crystallinity and crystal thickness of the PE block. For example, the incorporation of 15 wt % of a hydrogenated poly(norbornyl norbornene) block (T-g = 115 degrees C) into a PE diblock copolymer, cooled from the melt at similar to 1 degrees C/min, doubles the yield stress (from similar to 30 to similar to 60 MPa) and tensile modulus (from similar to 1.5 to similar to 3.5 GPa) relative to the values for a PE homopolymer treated with the same thermal history. These property enhancements are closely associated with the composition of the amorphous layer between crystal lamellae and the spatial distribution of the glassy block within this layer. Finally, the ductility of these polymers at high strains is governed by the presence or absence of tie molecules, which can be correlated with the chain dimensions of the PE block in the melt and the distance between crystal lamellae.