This paper presents the results of investigations in the field of diffractive or 'binary' computer-generated optics for the infra-red region of the spectrum. The problem of a CO2-laser beam focusing into a complicated focal domain is considered in detail. Special ray-tracing methods are elaborated to calculate the new analytic functions of diffractive optical elements, called focusators. The development of IR focusators into a ring, uniform planar spots, segments of a straight line, and other focal domains for the CO2 lasers powered from several watts up to 3 kW is reported. Reflective-type focusators are manufactured by a specific microrelief technology that has some features in common with normal microelectronic technology. Experimental results for focused-beam interaction with rubber, wood, fabric, and plastics are presented for the case of a 30-W laser. Effective laser heat-hardening of steel is achieved by 3-kW CO2 laser by means of a computer-generated reflective focusator.