New technology applications require new types of x-ray mirrors, in particular, mirrors working at different grazing angles. The angular range of standard x-ray mirrors is rather narrow and they cannot provide effective collimating and focusing of x-ray beams. It is shown that the needle optimization technique can be effectively applied to the design of x-ray mirrors with an extended angular range. Experimental results confirm a practical reproducibility of the designs obtained using this procedure.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.