Because of their distinct chemical signatures, ocean-island and mid-ocean-ridge basalts are traditionally inferred to arise from separate, isolated reservoirs in the Earth's mantle. Such mantle reservoir models, however, typically satisfy geochemical constraints, but not geophysical observations. Here we propose an alternative hypothesis that, rather than being divided into isolated reservoirs, the mantle is filtered at the 410-km-deep discontinuity. We propose that, as the ascending ambient mantle (forced up by the downward flux of subducting slabs) rises out of the high-water-solubility transition zone (between the 660 km and 410 km discontinuities) into the low-solubility upper mantle above 410 km, it undergoes dehydration-induced partial melting that filters out incompatible elements. The filtered, dry and depleted solid phase continues to rise to become the source material for mid-ocean-ridge basalts. The wet, enriched melt residue may be denser than the surrounding solid and accordingly trapped at the 410 km boundary until slab entrainment returns it to the deeper mantle. The filter could be suppressed for both mantle plumes (which therefore generate wetter and more enriched ocean-island basalts) as well as the hotter Archaean mantle (thereby allowing for early production of enriched continental crust). We propose that the transition-zone water-filter model can explain many geochemical observations while avoiding the major pitfalls of invoking isolated mantle reservoirs.