Method for cooling a synthesis gas which has been generated by catalytic steam reforming of a hydrocarbon-containing feed gas and has been cooled by heat exchange with boiler feed water to convert it into vapour, with the resulting aqueous condensate being separated off, cooled and treated in a plant for catalytic conversion of carbon monoxide with steam into hydrogen and carbon dioxide, comprising the following method steps: (a) heat exchange of the synthesis gas with the hydrocarbon-containing feed gas, (b) introduction of boiler feed water into a degasification plant comprising a feed water tank, wherein the boiler feed water is not preheated by heat exchange with the synthesis gas before the introduction into the degasification plant, wherein for its preliminary degasification the boiler feed water flows into the feed water tank, via a dome installed on the feed water tank, in countercurrent to steam rising out of the feed water tank, and wherein the steam, with the gases absorbed from the feed water, is discharged from the degasification plant and from the method for further treatment, (c) heat exchange of the synthesis gas with the boiler feed water degassed in the degasification plant, (d) heat exchange of at least a part of the synthesis gas with the boiler feed water contained in the feed water tank of the degasification plant, (e) heat exchange of the synthesis gas with the ambient air, (f) precipitation of condensate out of the synthesis gas and introduction of the condensate into the degasification plant, wherein for preliminary degasification the condensate flows into the feed water tank a dome installed on the feed water tank in countercurrent to steam rising out of the feed water tank, and wherein the steam, with the gases absorbed from the condensate, is discharged from the degasification plant and from the method for further treatment, (g) onward transfer of the synthesis gas for further treatment outside the method. (a) heat exchange of the synthesis gas with the hydrocarbon-containing feed gas, (b) introduction of boiler feed water into a degasification plant comprising a feed water tank, wherein the boiler feed water is not preheated by heat exchange with the synthesis gas before the introduction into the degasification plant, wherein for its preliminary degasification the boiler feed water flows into the feed water tank, via a dome installed on the feed water tank, in countercurrent to steam rising out of the feed water tank, and wherein the steam, with the gases absorbed from the feed water, is discharged from the degasification plant and from the method for further treatment, (c) heat exchange of the synthesis gas with the boiler feed water degassed in the degasification plant, (d) heat exchange of at least a part of the synthesis gas with the boiler feed water contained in the feed water tank of the degasification plant, (e) heat exchange of the synthesis gas with the ambient air, (f) precipitation of condensate out of the synthesis gas and introduction of the condensate into the degasification plant, wherein for preliminary degasification the condensate flows into the feed water tank a dome installed on the feed water tank in countercurrent to steam rising out of the feed water tank, and wherein the steam, with the gases absorbed from the condensate, is discharged from the degasification plant and from the method for further treatment, (g) onward transfer of the synthesis gas for further treatment outside the method.