High (3)He/(4)He ratios sampled at many ocean islands are usually attributed to an essentially undegassed lower-mantle reservoir with high (3)He concentrations. A large and mostly undegassed mantle reservoir is also required to balance the Earth's (40)Ar budget, because only half of the (40)Ar produced from the radioactive decay of (40)K is accounted for by the atmosphere and upper mantle. However, geophysical and geochemical observations suggest slab subduction into the lower mantle, implying that most or all of Earth's mantle should have been processed by partial melting beneath mid-ocean ridges and hotspot volcanoes. This should have left noble gases in both the upper and the lower mantle extensively outgassed, contrary to expectations from (3)He/(4)He ratios and the Earth's (40)Ar budget. Here we suggest a simple solution: recycling and mixing of noble-gas-depleted slabs dilutes the concentrations of noble gases in the mantle, thereby decreasing the rate of mantle degassing and leaving significant amounts of noble gases in the processed mantle. As a result, even when the mass flux across the 660-km seismic discontinuity is equivalent to approximately one lower-mantle mass over the Earth's history, high (3)He contents, high (3)He/(4)He ratios and (40)Ar concentrations high enough to satisfy the (40)Ar mass balance of the Earth can be preserved in the lower mantle. The differences in (3)He/(4)He ratios between mid-ocean-ridge basalts and ocean island basalts, as well as high concentrations of (3)He and (40)Ar in the mantle source of ocean island basalts, can be explained within the framework of different processing rates for the upper and the lower mantle. Hence, to preserve primitive noble gas signatures, we find no need for hidden reservoirs or convective isolation of the lower mantle for any length of time.