Chemical inertness and surface volatility, combined with low abundance, have made the rare (noble) gases a unique trace-elemental and isotopic system for constraining the formation and evolution of the solid Earth and its atmosphere(1-3). Here I examine the implications of recent high-pressure measurements of the melting temperatures of heavy rare-gas solids-argon, krypton and xenon-with new diamond-anvil cell methods, together with their pressure-volume relationship, for the total rare-gas inventory of the Earth since its formation. The solid-liquid (melting) transition in these rare-gas solids rises significantly with pressure in the 50 GPa range(4,5), such that melting temperatures will exceed the geotherm at pressures of the Earth's transition zone;md lower mantle (depths greater than 410-670 km), The densities of condensed rare-gas solids obtained from recent pressure-volume measurements at high compressions also exceed Earth's mantle and core densities. These pressure-induced changes in the physical properties of rare-gas solids, combined with their expected low solubilities and diffusional growth mechanisms, suggest that dense solid or fluid inclusions of rare gases-initially at nanometre scales-would have formed in the Earth's interior and may have resulted in incomplete planetary degassing, Separation of dense solid inclusions into deeper regions during early planet formation could provide a straightforward explanation for the unexpectedly low absolute abundance of xenon observed in the atmospheres of both Earth and Mars.