In a highly efficient recuperator burner, which comprises at least one combustion chamber for warm-up operation and is otherwise set up for FLOX® operation, and a recuperator for preheating combustion air by means of thermal exhaust gas energy in a counter-current heat exchange mode via heat exchanger pipes, each heat exchanger pipe has, in a heat exchange section thereof, a flattened gap cross-section and, at its end facing a volume to be heated, a nozzle cross-section, which differs from the flattened gap cross-section of the heat exchanger pipe.