Accurately controlling light emission using nano- and microstructured lenses and antennas is an active field of research. Dielectrics are especially attractive lens materials due to their low optical losses over a broad bandwidth. In this work we measure highly directional light emission from patterned quantum dots (QDs) aligned underneath all-dielectric nanostructured microlenses. The lenses are designed with an evolutionary algorithm and have a theoretical directivity of 160. The fabricated structures demonstrate an experimental full directivity of 61 ± 3, three times higher than what has been estimated before, with a beaming half-angle of 2.6°. This high value compared to previous works is achieved via three mechanisms. First, direct electron beam patterning of QD emitters and alignment markers allowed for more localized emission and better emitter-lens alignment. Second, the lens fabrication was refined to minimize distortions between the designed shape and the final structure. Finally, a new measurement technique was developed that combines integrating sphere microscopy with Fourier microscopy. This enables complete directivity measurements, contrary to other reported values, which are typically only partial directivities or estimates of the full directivity that rely partly on simulations. The experimentally measured values of the complete directivity were higher than predicted by combining simulations with partial directivity measurements. High directivity was obtained from three different materials (cadmium-selenide-based QDs and two lead halide perovskite materials), emitting at 520, 620, and 700 nm, by scaling the lens size according to the emission wavelength.