Multilayer Laue lenses are volume diffraction elements for the efficient focusing of X-rays. With a new manufacturing technique that we introduced, it is possible to fabricate lenses of sufficiently high numerical aperture (NA) to achieve focal spot sizes below 10 nm. The alternating layers of the materials that form the lens must span a broad range of thicknesses on the nanometer scale to achieve the necessary range of X-ray deflection angles required to achieve a high NA. This poses a challenge to both the accuracy of the deposition process and the control of the materials properties, which often vary with layer thickness. We introduced a new pair of materials-tungsten carbide and silicon carbide-to prepare layered structures with smooth and sharp interfaces and with no material phase transitions that hampered the manufacture of previous lenses. Using a pair of multilayer Laue lenses (MLLs) fabricated from this system, we achieved a two-dimensional focus of 8.4 x 6.8 nm(2) at a photon energy of 16.3 keV with high diffraction efficiency and demonstrated scanning-based imaging of samples with a resolution well below 10 nm. The high NA also allowed projection holographic imaging with strong phase contrast over a large range of magnifications. An error analysis indicates the possibility of achieving 1 nm focusing.