 In 1973-74 Wrexham reached the last eight of the FA Cup, beating the soon-to-be-crowned Second Division champions Middlesbrough and top-flight Southampton before bowing 1–0 to Burnley, then among the top six clubs in the country.Then in 1975-76 May was an inspirational part of the side which made it to the quarter-finals of the European Cup- Winners' Cup, where they went down 2–1 on aggregate to the illustrious Belgians, Anderlecht.The following August, aged 33 and having missed only 34 League games in his eight seasons in North Wales, he was freed to join Fourth Division Swansea City having spent the 1975 summer with NASL side Chicago Sting.