A vapor-compression distiller includes a rotary heat exchanger. A reciprocating compressor (26) maintains a pressure difference between the compressor's evaporation chambers (46) and its condensation chambers (44). The compressor is assembled in a common rotating assembly with the compressor, so the distiller does not need rotating seals between the compressor and heat exchanger. The compressor includes two pistons (56 and 58) driven in opposite directions in a rotating piston chamber (54). The directions in which they thereby reciprocate are substantially parallel to the rotating assembly's axis.