Modelling tritium retention in radiation-damaged pure-tungsten samples, the concentration of deuterium retained in the tungsten-ion-induced damage zone decreases with increasing exposure temperature; whereas for a similarly treated tungsten–rhenium alloy, it can drop significantly faster than in pure tungsten, given sufficiently high temperatures. In contrast, similar changes in retention behaviour were not observed in undamaged samples. Based on these findings, as well as on corresponding previous TEM results, it is concluded that the concentration of high-energy radiation-induced defects responsible for trapping of deuterium is lower in the alloy than in pure tungsten. Therefore, a small amount of transmutation rhenium in damaged tungsten should be able to keep tritium retention to a low level in ITER.