A system for precision cleaning of contaminants from the surface of a substrate, such as delicate surfaces or precision parts, utilizing streams of carbon dioxide snow or other cleaning gas. The system includes an enclosed or sealed cleaning container in which at least one jet spray device is housed for directing a stream of cleaning snow against the surface to be cleaned. During cleaning, the cleaning container holding the substrate to be cleaned is maintained under a vacuum or, optionally, at ambient pressure, filled with a clean dry gas. The dislodged contaminants and spent snow are removed from the cleaning zone and disposed of or recycled. Cleaning is accomplished by pulsed application of the cleaning snow in combination with intermittent or continuous heating of the surface so that the surface is at an elevated temperature prior to and during each application of cleaning snow. The jet spray devices which are utilized in the system are oriented so that the cleaning snow streams contact planar surfaces at grazing angles of 5 to 45 degrees. When non-planar parts are being cleaned, the jet spray devices are adjusted to provide an angle of about 45 to 90 degrees. Monitoring of the cleanliness of the parts is accomplished during the cleaning process, by a light scatter method or by a particle monitor and residual gas analysis of the exhaust gas or other analysis of the exhaust gas. The system is particularly useful in removing contaminants from the delicate surfaces or precision parts which are utilized in precision optical and electronic devices.