Speyrer was born in Port Arthur, Texas on April 29, 1949, but spent some time growing up in Brownsville, where he got the nickname "Cotton" due to his white hair.
[3] Speyrer was a tailback in high school, who scored rushing, receiving and even passing, as well as while returning kickoffs in his senior year (1967).
[11][12] Speyrer shared the Cotton Bowl MVP honors with teammates Tom Campbell and quarterback James Street.
[16] Texas won two historic games that season, against Arkansas in December, and the January 1, 1970 Cotton Bowl against the University of Notre Dame.
Starting on their own 24-yard line, the Longhorns embarked upon a fourth-quarter, 17-play march that included a pair of fourth-and-two conversions, the last coming at the Notre Dame 10 when James Street completed a clutch (though almost too short) pass to a turning and diving Speyrer that took the Horns to the two.
From there, it took three plays before Billy Dale pushed the ball over the goal line to cement UT's second national title—Texas 21, Notre Dame 17.
[27][28] The catch and victory was a key part of Texas finishing the regular season undefeated where they were awarded their 3rd National title (1963, 1969 & 1970) by the UPI Coach's Poll.
[30] He was traded along with a 1973 first-rounder (25th overall–traded to San Diego Chargers for Marty Domres) from the Redskins to the Baltimore Colts for Roy Jefferson and ninth-round draft picks in 1973 (218th overall–Rick Galbos) and 1974 (213th overall–traded to Los Angeles Rams for Joe Sweet) on July 31, 1971.
He left Redskins training camp during the 2nd week after complaining that he wasn't getting enough chances to play and was traded to Miami for an undisclosed future pick.
[citation needed] Two days after joining the Dolphins he led them to a 20-17 victory over the Saints after catching three passes of longer than 50 yards in an exhibition game.