The self-pumping concept was proposed as a means of simplifying the impurity control system in a fusion reactor. The idea is to remove helium in-situ by trapping in freshly deposited metal surface layers of a limiter or divertor. Trapping material is added to the plasma scrape-off or edge region where it is transported to the wall. Some of the key issues for this concept are the tritium inventory in the trapping material and the permeation of protium and recycling of tritium. These quantities are shown to be acceptable for the reference design. The tritium issues for a helium-cooled solid breeder reactor design with vanadium alloy as a structural material are also examined. Models are presented for tritium permeation and inventory calculation for structure materials with the effect of a thin laver of coating material.