In 1978, Gossett was selected in the fifth round by the New York Mets and played in their farm system for two seasons as an outfielder and third baseman.
[2] Gossett was signed as an undrafted free agent by the Dallas Cowboys after the 1980 NFL draft on April 30.
[3] On November 5, 1981, he was signed by the Kansas City Chiefs to replace an injured Bob Grupp, finishing with a 39.3-yard punt average.
[4] In 1982, he was cut before the seventh game of the season and surprisingly brought back a week later after a terrible showing by rookie Case deBruijn against the Denver Broncos.
[6] On August 29, 1983, he was released after losing a preseason competition with rookie fifth round draft choice Jim Arnold.
[7] On August 31, 1983, he was claimed off waivers by the Cleveland Browns, to replace Steve Cox, who was recovering from a surgery to remove a blockage between his brain and his spinal cord.
[10] In 1987, he played in the first 5 games of the season, before being replaced with rookie punter George Winslow and released on November 18.
In 1988, the team drafted punter Greg Montgomery in the third round and traded Gossett to the Los Angeles Raiders on August 15, in exchange for undisclosed future considerations.
In 1991, he switched his jersey number from 6 to 7, and went on to average a career-high 44.2 yards per punt, while being named an All-Pro and selected to the Pro Bowl roster.