[4] Minter took part at the 1970 European Junior Championships at the middleweight division, but in the very first fight he was stopped in the 2-nd round by Vyacheslav Lemeshev (USSR).

[6] He won a bronze medal at the 1972 Munich Olympic Games in the light-middleweight classification, losing in the semifinal to Dieter Kottysch of West Germany by a 3-2 marginal decision which was hotly disputed.

[9] In 1975, he won four fights in a row, including another bout in Hamburg and, by the end of the year, he challenged Kevin Finnegan for the British Middleweight title, winning it by a 15-round decision.

[9] Minter returned to top ten challenger status by upsetting the former World Welterweight and Light Middleweight Champion Emile Griffith with a ten-round decision win in Monte Carlo,[9] but then he lost his European title to Gratien Tonna by a knockout in eight at Milan.

On 15 February, at the Muhammad Ali–Leon Spinks I undercard in Las Vegas, Nevada, he won his first bout in the United States by knocking out Sandy Torres in five.

On 16 March 1980, in Las Vegas, he was given a shot at World Middleweight Champion Vito Antuofermo's title at Caesars Palace.

[9] On 27 September 1980, Minter's short run as world champion came to an abrupt end when he was stopped on cuts in the third round against 'Marvelous' Marvin Hagler at Wembley Arena in London.