Closed-cell extruded foam extruded foam with density in the range from 20 to 150 g/l and with a cell number in the range from 1 to 30 cells per mm is obtainable via (a) heating of a polymer component P, formed from P1) from 80 to 100% by weight (based on P) of one or more styrene-acrylonitrile copolymers (SAN), comprising a1) from 18 to 40% by weight (based on SAN) of copolymerized acrylonitrile, a2) from 60 to 82% by weight (based on SAN) of copolymerized styrene, and a3) from 0 to 22% by weight (based on SAN) of at least one copolymerized monomer from the group consisting of alkyl(meth)acrylates, (meth)acrylic acid, maleic anhydride and maleimides, P2) from 0 to 20% by weight (based on P) of one or more thermoplastic polymers from the group consisting of styrene copolymers, polyolefins, polyacrylates, polycarbonates (PC), polyesters, polyamides, polyether sulfones (PES), polyether ketones (PEK), and polyether sulfides, to form a polymer melt, (b) introduction of from 1 to 12% by weight (based on P) of a blowing agent component (T), which comprises less than 0.2% by weight of water (based on P), comprising b1) from 15 to 95% by weight (based on T) of carbon dioxide and b2) from 5 to 85% by weight (based on T) of one or more co-blowing agents selected from the group consisting of C1-C4 alcohols and C1-C4 carbonyl compounds, into the polymer melt to form a foamable melt, (c) extrusion of the foamable melt into a region of relatively low pressure, with foaming to give the extruded foam, (d) if appropriate, addition of additives to the polymer component (P) in at least