As a sophomore, he intercepted 3 passes in a game against Texas Christian University, tying a single-game school record.

As a senior, he was named a co-captain and although he was limited with a pinched nerve in his neck, he received All-Southwest Conference and honorable-mention All-American honors.

He wasn't selected because he suffered a pinched nerve in his shoulder as a senior, which affected his play and earned him a reputation for not being aggressive.

He was so impressive in training camp, that he became the third rookie in Cowboys history to begin the season as a starter at free safety, after Randy Hughes suffered a dislocated right shoulder and Dextor Clinkscale an Achilles injury in pre-season.

[1] He was a playmaker from the start, intercepting a Joe Theismann pass in the first quarter of a 26–10 win against the Washington Redskins in the season opener.

Against the Tampa Bay Buccaneers, he had 15 tackles (club season high), he forced a fumble and recovered another one at the two-yard line with five seconds left to preserve a 14-9 win.

Against the New Orleans Saints, Downs helped the team rally back from a 27-6 fourth-quarter deficit to win 30–27 in overtime, by making 9 tackles, 2 interceptions, one pass defensed, one fumble recovery and also recovered a blocked punt.

On September 26, 1989, he was signed as a free agent by the Phoenix Cardinals, after Lonnie Young broke his left shoulder in the season-opener.