The invention relates to apparatus and a method for preparing a fine oil mist, in particular to be fed into tool lubrication ducts of a CNC machine tool. The apparatus is turned ON/OFF solely using the standardized machine commands M08 (“Cooling lubricant ON”) and M09 (“Cooling lubricant OFF”). The control/regulation of the tools' aerosol supplies then will be fully automatic. It involves—contrary to known quantitative regulations—a simple regulation by means of aerosol pressure values. When starting the apparatus or following a change of tools, all aerosol pumps are operating, including, where tools exhibit cross-sectionally large boreholes, an oil over-enriching pump. At least one aerosol pump operates when regulated within a range of supply pressures. When the upper pressure value of the supply pressure range is exceeded, the pump(s) shut(s) down until the aerosol sup[ply has been exhausted and will turn ON again when the lower pressure value of the supply pressure range is crossed downward because of aerosol consumption.