The invention relates to a process for preparing isocyanates by reacting the corresponding amines with phosgene in the gas phase, in the presence or absence of an inert medium, which comprises the following steps: (a) vaporization of the amine in a vaporizer, (b) superheating of the amine, (c) mixing of the gaseous amine with the phosgene and introduction into a reaction zone, (d) reaction of amine and phosgene to give isocyanate in the reaction zone, with a reaction mixture comprising isocyanate and hydrogen chloride being formed, (e) cooling of the reaction mixture comprising isocyanate and hydrogen chloride, wherein the vaporizer comprises a vessel in which tubes through which a heating medium flows are comprised, where number and diameter of the tubes are designed so that the tubes have a specific heat transfer area based on the volume through which the amine flows of at least 300 m2/m3.