Experimental data on the effect of irradiation and anneal treatments on the electric characteristics of high-voltage power static induction transistors (BSITS) are given. The treatments include bombardment by high-energy electrons and a subsequent isothermal treatment. The anneal behaviour of radiation-induced centres in the operating elements of BSITS is discussed. A criterion of preference for the centres, which control lifetimes, is suggested. The criterion of preference fits the A-centre. In addition, it is shown that the irradiation/anneal processing gives the best improvement of the semiconductor device characteristics when the phosphorus impurity concentration greatly exceeds the oxygen concentration in the heavily doped Si substrate and the oxygen content greatly exceeds the carbon content in the epilayer.