In that race he originally finished second by the smallest margin ever to decide an Olympic swimming final (one hundredth of a second), but was later awarded the gold medal after the victor, American Rick DeMont, an asthmatic, was disqualified after his post-race urinalysis tested positive for traces of the banned substance ephedrine contained in his prescription asthma medication, Marax.

[1] The second of three brothers, Cooper was born in Singapore to Australian parents but moved with his family to Rockhampton, Queensland at the age of five.

For the next three years his father entered an unsettled phase, during which time he and Brad lived in a dozen men's boarding houses and hostels in Brisbane and Sydney.

In 1970, at age 15, at the national open championships, Cooper came second in both the 100 m and 200 m backstroke, putting him briefly in contention for that year's Commonwealth Games team.

He also came second in the 400 m freestyle behind fellow Talbot swimmer Graham Windeatt, surpassing the previous Australian record.

Within a month, at the Australian Championships in Brisbane, he won the 400 m and 1500 m freestyle events and the 100 m and 200 m backstroke, showing versatility over a large range of distances.

[2] After the Olympics, Talbot left to become a coach in Canada, forcing Cooper to return to Brisbane to train with Harry Gallagher.

Cooper was then awarded a swimming scholarship to Miami University, but was unable to enrol as he had not finished his secondary education in Australia.