The invention relates to a heat exchanger, in particular, an evaporator (1), in particular for a motor vehicle air-conditioner, with a number of closely arranged refrigerant tubes and at least one cold reservoir (4), in which a refrigerant medium is provided. The evaporator (1) comprises two parallel regions (1′ and 1″) running across the total width, the first region (V) corresponding to a conventional evaporator in design, the cold reservoir (4) being arranged in a separate second region (1″), through which at least a partial flow of refrigerant can flow which also flows through at least a part of the first region (1′) and the first and the second region are connected to each other by at least one overflow opening (13).