The present invention is a method and system for the drilling of holes in a workpiece within a diameter range of 20 μm to 500 μm by means of laser radiation. The invention utilizes the beam quality of a laser beam as well as: the polarization of the laser radiation; the parameters of the impulses of the laser used; and, the type and pressure of the process gas used. The method and system utilize means for focusing laser radiation, in particular the ratio of the beam diameter at the site of the focusing element and its focal distance, and wherein the focusing is done in coordination with the beam quality number and wave length and other factors. A first working gas supports the formation of the hole shape and accelerates the drilling process; and, a second working gas is utilized to improve the surface quality of the drilling walls.