A distillation unit (10) employs a fluid circuit (FIG. 8) in which a counterflow heat exchanger (102, 104, 106, 108, 110) transfers heat from condensate and concentrate to feed liquid to be distilled. The pumping system (100, 238) that drives fluid through the circuit is arranged to keep the pressure in the counterflow heat exchanger's condensate higher than that in its feed-liquid passage. This tends to discourage the contamination that could otherwise occur in the concentrate if the fluid isolation ordinarily maintained between those passages is compromised.