A gasification reactor for producing crude gas, containing CO or H2, by gasification of ash-containing fuel with oxygen-containing gas, at temperatures above the melting temperature of the ash, has a reaction chamber formed by a membrane wall through which coolant flows, within a pressure container, is provided, with a narrowing transition channel into a gas cooling chamber, and spin-reducing, cooled bulkheads in the transition channel. The, wall that carries the bulkheads makes a transition, below the bulkheads, into a cylinder wall that is reduced in diameter, by way of a step having a corrugated surface. The cylinder wall, which is reduced in diameter, is enclosed by a further cylindrical wall, which is enlarged in diameter, which wall forms a second slag drip edge at its end, in the direction of gravity. The further cylindrical wall is disposed to be adjustable in its vertical position, with reference to the first drip edge.