Process for separating butenes from a C4-hydrocarbon stream which contains at least butenes and butanes by extractive distillation with a solvent, wherein the process comprises the steps of: a. at least partially evaporating the liquid C4-hydrocarbon stream in a feed evaporator, supplying the gaseous C4-hydrocarbon stream and supplying the liquid solvent to a liquid distributor above the C4-hydrocarbon stream to an absorber which comprises more than two random-packing beds and in which the C4-hydrocarbon stream and the solvent are contacted with one another to transfer predominantly butenes from the C4-hydrocarbon stream to the solvent, wherein the thus-laden solvent is collected in a liquid collector of the absorber, passed through an absorber evaporator and then passed into the bottom of the absorber below the liquid collector to outgas predominantly butanes from the laden solvent, wherein the laden solvent is subsequently passed to a desorber as bottoms stream and wherein a stream enriched in butanes relative to the employed C4-hydrocarbon stream is obtained at the top of the absorber and at least partially condensed and a portion of the condensate is returned to the top of the absorber as reflux; b. supplying the supplying the laden solvent, preferably NMP, to the desorber, which is at an elevated temperature and preferably a lower pressure relative to the absorber and in which the butenes are separated from the solvent, preferably NMP, to obtain at the top of the desorber a stream enriched in butenes and to obtain at the bottom of the desorber the solvent at least partially freed of butenes, preferably NMP, wherein the solvent at least partially freed of butenes, preferably NMP, is collected in a liquid collector of the desorber, passed through a desorber evaporator and then passed into the bottom of the desorber below the liquid collector to outgas any butenes remaining in the solvent and wherein the solvent, preferably NMP, is subsequently recycled to the absorber as bottoms stream; characterized in that the heat of the solvent withdrawn as a bottoms stream of the desorber is used for heat integration by employing the heat of the solvent in at least one respective heat exchanger for preheating the laden solvent passed to the desorber, for evaporation in the absorber evaporator and for evaporation of the liquid C4-hydrocarbon stream and in that at least a portion of a liquid phase is withdrawn at the liquid distributor above the first or second random-packing bed and separated into a heavy liquid phase and a light liquid phase in a decanter, of which the heavy liquid phase is returned to the absorber and/or the reflux in the absorber is withdrawn from the absorber via a runoff cup, mixed with the liquid solvent in a static mixer and then, with the liquid solvent, supplied to the liquid distributor above the first random-packing bed. a. at least partially evaporating the liquid C4-hydrocarbon stream in a feed evaporator, supplying the gaseous C4-hydrocarbon stream and supplying the liquid solvent to a liquid distributor above the C4-hydrocarbon stream to an absorber which comprises more than two random-packing beds and in which the C4-hydrocarbon stream and the solvent are contacted with one another to transfer predominantly butenes from the C4-hydrocarbon stream to the solvent, wherein the thus-laden solvent is collected in a liquid collector of the absorber, passed through an absorber evaporator and then passed into the bottom of the absorber below the liquid collector to outgas predominantly butanes from the laden solvent, wherein the laden solvent is subsequently passed to a desorber as bottoms stream and wherein a stream enriched in butanes relative to the employed C4-hydrocarbon stream is obtained at the top of the absorber and at least partially condensed and a portion of the condensate is returned to the top of the absorber as reflux; b. supplying the supplying the laden solvent, preferably NMP, to the desorber, which is at an elevated temperature and preferably a lower pressure relative to the absorber and in which the butenes are separated from the solvent, preferably NMP, to obtain at the top of the desorber a stream enriched in butenes and to obtain at the bottom of the desorber the solvent at least partially freed of butenes, preferably NMP, wherein the solvent at least partially freed of butenes, preferably NMP, is collected in a liquid collector of the desorber, passed through a desorber evaporator and then passed into the bottom of the desorber below the liquid collector to outgas any butenes remaining in the solvent and wherein the solvent, preferably NMP, is subsequently recycled to the absorber as bottoms stream; characterized in that the heat of the solvent withdrawn as a bottoms stream of the desorber is used for heat integration by employing the heat of the solvent in at least one respective heat exchanger for preheating the laden solvent passed to the desorber, for evaporation in the absorber evaporator and for evaporation of the liquid C4-hydrocarbon stream and in that at least a portion of a liquid phase is withdrawn at the liquid distributor above the first or second random-packing bed and separated into a heavy liquid phase and a light liquid phase in a decanter, of which the heavy liquid phase is returned to the absorber and/or the reflux in the absorber is withdrawn from the absorber via a runoff cup, mixed with the liquid solvent in a static mixer and then, with the liquid solvent, supplied to the liquid distributor above the first random-packing bed.