Laser micromachining has been proved to be a useful tool for the formation of microstructures in semiconductor and optical materials. It is also widely adopted for dicing of light-emitting diode chips. The authors propose a modified laser micromachining setup which enables three-dimensional structures to be formed. A mirror is inserted in the optical path between the focusing optics and the machining plane so that the beam strikes the sample at an oblique angle. By translating and/or rotating the sample as micromachining is carried out, various three-dimensional structures such as a pyramid or a conic section can be obtained. Trenches as small as 10 mu m on sapphire have been realized with nanosecond ultraviolet laser pulses. Laser-induced damage, due to resolidification of the ablation melt, accumulates with increasing scans of the beam; it can be removed by chemical and mechanical treatment.