After his unconvincing performances with the bat in the South African Tests, Simpson needed runs at the start of the 1958–59 season to retain his position in the national team for the Ashes series against England. His first two matches of the season were for Western Australia and a Western Australia Combined XI against the Englishmen, and he scored 60 and 17. In three further Shield matches, he continued his habit of not converting starts into larger scores, registering scores of between 31 and 67 in all six innings with three half-centuries. Up to this point, he had scored 364 runs at 52.00, and Simpson was selected for the Australian XI match against May's Englishmen, effectively a dress rehearsal for the Tests. He failed in both innings with two and a duck, and the hosts were crushed by 345 runs. Simpson was overlooked for selection for the First Test at Brisbane against England. Norm O'Neill, who had scored 1,003 runs at 83.75 in the previous season, while Simpson was in South Africa, took his middle-order position. Peter Burge failed in the First Test, resulting in Simpson's recall for the Second Test at Melbourne. Simpson made a duck in his only innings as Australia won by eight wickets and was subsequently omitted for the remainder of the series. At the time, Australia had three all rounders who were capable with the bat:Ken Mackay, Richie Benaud and Alan Davidson. This meant that Australia needed only five specialist batsmen and in the Fifth Test of the series, only four were used in order to accommodate an extra bowler. Simpson was facing heavy competition for a Test position. Simpson scored 91 runs in four innings in the remainder of the season, which was not enough for him to force his way back into the Test team. It was another sparse summer with the ball for Simpson, who took two wickets at 41.50.