Lensless x-ray imaging is a promising method to determine the three-dimensional structure of material science and biological specimens at the nanoscale. The development of this technique is strongly related to the optimization of x-ray optics since the image formation and object reconstruction depend significantly on the properties of the illumination wave-field. Waveguide optics act as quasi-point sources and enable the spatial and coherent filtering of x-ray beams. Up to now, x-ray waveguides were severely limited in transmission and flux, restricting their use to high-contrast test structures with moderate resolution and long accumulation times. To overcome these limitations, a novel waveguide design with an optimized refractive index profile is presented which significantly minimizes the absorption of the modes propagating inside the waveguide. Experimental results along with simulations show that these two-component planar x-ray waveguides provide small beam cross-sections along with a high photon flux at the exit. By a serial arrangement of two waveguide slices an optimized illumination source has been developed for high-resolution microscopy, as demonstrated in proof-of-concept imaging experiments.