The focusing efficiency of conventional diffractive x-ray lenses is fundamentally limited due to their symmetric binary structures and the corresponding symmetry of their focusing and defocusing diffraction orders. Fresnel zone plates with asymmetric structure profiles can break this limitation; yet existing implementations compromise either on resolution, ease of use, or stability. We present a new way for the fabrication of such blazed lenses by patterning two complementary binary Fresnel zone plates on the front and back sides of the same membrane chip to provide a compact, inherently stable, single-chip device. The presented blazed double-sided zone plates with 200 nm smallest halfpitch provide up to 54.7% focusing efficiency at 6.2 keV, which is clearly beyond the value obtainable by their binary counterparts.