It is well known that a metal tip blunts if it is heated in vacuum. Sharpening may occur in the case of an evaporation of the tip material. To test this, molybdenum tips were heated in vacuum. A typical result: at 2400K, the tip radius decreases from 8 mu m to 0.3 mu m thus confirming the hypothesis. Measured and calculated final radii agree roughly. The pure material evaporation can be replaced by a surface reaction followed by the evaporation of the reaction products. This is shown on tungsten tips heated (1750K) in the presence of oxygen (0.5 mTorr). The evaporation of tungsten oxides results in a sharpening to a radius to 0.05 mu m. Under special conditions, in connection with the formation of solid drops, radii down to 0.01 mu m are obtained.