[3] Elliott was signed as an undrafted free agent by the Dallas Cowboys after the 1992 NFL draft, to compete as the replacement for kicker Ken Willis.
[4] He recovered from a pulled groin muscle in training camp, to be named the starter over Brad Daluiso.
He started the regular season slowly until hitting 13 straight field goals and registering 27 touchbacks, which at the time were both franchise records.
He missed two field goals in the 10–13 loss against the Buffalo Bills in the second game, contributing to a 0–2 start.
But he is best remembered for missing three field goal attempts from 35, 39, and 42 yards in a 10–7 playoff loss to the Indianapolis Colts in January 1996.
On February 16, 1996, the Chiefs decided not to make him a qualifying offer as a restricted free agent, effectively releasing him, even though he had an 81.7% field goal accuracy during his two seasons, ranking as the second-most accurate kicker in Chiefs history.