An economical and commercially practical reverse-osmosis water purifier system which has no back pressure acting against the semipermeable membrane, so that the filtering rate is maximized. Furthermore, the supply of tap water to the system is shut off automatically as soon as the pure water storage tank is full, use of water thus being greatly reduced. These, and other major advantages, are achieved despite the fact that there is only a single tube extending to the faucet, automatic ice-maker, refrigerated drinking fountain or other point of use.The system uses rugged, long-lasting and economical diaphragm valves, which eliminates the need for sliding seals. Thus, it becomes highly practical to injection-mold the valves of plastic.The long-standing major problem of plugging or fouling of the constricted outlet for waste water is eliminated at low cost and with very little use of water. What water is used provides not only cleaning of the constriction region but also a partial flushing of the filter membrane. These results are achieved by means of a self-cleaning constrictor valve having a predetermined flow area which may be made as small as the manufacturer desires.In one embodiment, a valve is provided to automatically stop the outflow of squeeze water while the faucet is in open condition. This saves additional water and also makes it possible to build up a relatively high pure-water pressure even when the inlet pressure is less than average.