The tritium inventory of an experimental fusion reactor like ITER is determined by a broad range of influential factors. The tritium retention in the vacuum system is one important contribution to the overall tritium inventory. The high vacuum system for ITER is based on a set of cryogenic pumps, and sees the whole spectrum of tritiated gas species. The cryopumps are accumulation pumps; thus, the semi-permanent tritium inventory present in them is governed by the effectiveness of pump regeneration. Moreover, a permanent inventory background must also be envisaged. This paper delineates the staggered pump concept and a multi-stage regeneration scheme as main measures for step-wise minimisation of the tritium inventory in the high vacuum pump system and outlines the different contributions which add to it. By these methods, the 268 g of tritium inventory present after nominal long pulse operation of ITER, depending on the chosen fuelling case, can be reduced to 6 g in the pumps themselves, plus up to 100 g of codeposited tritium needing recovery clean-up.