Copper-containing catalysts for low temperature shift conversion at from 150.degree. to 300.degree. C. and under from 10 to 40 bar, which additionally contain aluminum and zinc, if necessary in the form of the compounds or oxides and are prepared by coprecipitation, the copper-containing catalysts containing potassium and having a BET surface area adapted to the potassium content, and the potassium content being brought to 0.1-3.0% by weight at a BET surface of from 30 to 160 m.sup.2 /g, are used for the preparation of hydrogen and carbon dioxide from carbon monoxide and water.