A method of distillation employing a heat pump (which may be driven by a compressor) using a vapor stream from within the distillation system as a heat source and a liquid stream from within the distillation system as a heat sink. The selection of heat-source vapors and heat-sink liquid is such that at least one is withdrawn from the phase-contracting region of the distillation system. The return of streams withdrawn from the phase-contacting region of the distillation system to the distillation system is such that at least one of the streams is returned at a temperature different from that of the point from which it was withdrawn, and all withdrawn streams are returned in manner such that a stream removed as vapor is returned at a point with a temperature at most that at the point it was withdrawn, and a stream removed as liquid is returned at a point with a temperature at least that at which it was withdrawn. Embodiments of the basic method where vapor only, liquid only, or both liquid and vapor are withdrawn from and returned to the phase-contacting region of the distillation system are considered. The impact of the invention is to reduce the heat requirement of distillation in exchange for an amount of work which is usually small because the temperature difference between heat sources and sinks is minimized. Combination of the basic distillation method with multi-effect distillation, convention overhead-to-reboiler heat pumped distillation, azeotropic and extractive distillation, and fermentative production of volatile compounds is described. A system specifically designed for the separation of ethanol-water mixtures which utilizes the present invention and extractive distillation in a system with extensive heat integration is presented.