At the 1958 British Empire and Commonwealth Games in Cardiff, Puckett competed in the men's six-mile race, finishing 12th, and in the marathon, placing 14th. Competing in the marathon at the 1960 Rome Olympics, Puckett finished in 51st place in a time of 2:37:36. Four years later in the same event at the 1964 Olympics in Tokyo, he ran 2:27:34 to finish 27th.