The 1973–74 season saw Wrexham change their badge from the Maelor crest to a brand new badge that had a lot more resemblance to the Welsh roots of the club, with three feathers on the top of the badge and two dragons, one on either side of the badge and facing inwards. This is still the present badge for today's team. This season also saw Wrexham reach the quarter-finals of the FA Cup in another cup run. After victories over Shrewsbury Town, Rotherham United, Middlesbrough, Crystal Palace and Southampton, their cup run finally came to end against first division side Burnley at Turf Moor, with just over 20,000 Wrexham fans present to watch the match. Also that season Wrexham just missed out on the promotion spots, finishing in 4th place at the end of the season.  1975–76 saw John Neal's starlets captained by Eddie May, again shocked the football world by reaching the quarter-finals of the European Cup Winners' Cup after another sparkling cup run and multiple defeats of higher quality opponents. In the first round Wrexham beat Swedish team Djurgårdens IF 3–2 on aggregate. They then managed to knock out Polish side Stal Rzeszow 3–1 on aggregate. Wrexham played Belgian champions Anderlecht in the quarter finals and narrowly lost 2–1 to the eventual winners of the competition. The 1976–77 season saw Wrexham again beat First Division opposition in both Cup competitions as they went on another cup run, defeating Tottenham Hotspur in the Football League Cup and Sunderland in the FA Cup, however the league season was a traumatic one as the club, on the verge of promotion to the second division with only four matches left to play, required just three points to reach their goal, and unbelievably they missed out after a poor run of form. Arfon Griffiths took over as player-manager for the 1977–78 season. They reached both the League and FA Cup quarter-finals that season, and Wrexham finally clinched promotion to the second division when they beat Rotherham United 7–1 at a packed Racecourse, and Wrexham went on to win the Third Division Championship that year. In the 1978–79 season Wrexham made it to the fourth round of the FA Cup where they narrowly lost to Tottenham Hotspur 3–2 in the replay after the first game finished 3–3, the Spurs team had stars amongst their ranks such as Ossie Ardiles, Ricky Villa and Glenn Hoddle in their team, and Wrexham were unfortunate to get knocked out.