Brady went in 1995 to the Jets, and he went at number 9. Cleveland had no pick anywhere near that.
I think you are wrong about Cleveland not being close in the 1995 draft they had the very next pick and traded down with San Francisco once Kyle Brady was selected by the Jets. As I can recall rumor had it that Cleveland was so
interested in obtaining Brady and that was another draft learning experience for the Cleveland Front Office. But here's a few links if you want to check out the story.
http://www.clevelandbrowns.com/team/history/90.php
http://www.sf49ers.com/history/draft-1990.php
http://nflhistory.net/shared/articles/news.asp?action=detail&article=75
7. Craig Powell, Round 1, 1995 – This pick was never supposed to be. The Browns originally had the 17th pick in the draft, and were going to select TE Kyle Brady from Penn State with it, but the NY Jets at number 16 shocked the world by taking Brady instead. In a moment of panic, Cleveland traded their pick to (ironically) Carmen Policy of the 49ers for later picks plus a 1996 first round pick, and were stuck with the Powell pick. Something did end up coming out of this, though not for Cleveland. The Baltimore Ravens used the 1996 first round selection to draft Ray Lewis.
1995
Round Player Position University Notes
1a Choice to San Francisco for 49ers’ 1995 1st [30th overall], 3rd [94th overall], 4th [119th overall] and 1996 1st round pick
1b Powell, Craig LB Ohio State [30th overall] Choice from San Francisco, see 1a
2 Choice to Philadelphia see 1994 round 2
3a Zeier, Eric QB Georgia [84th]
3b Frederick, Mike DE Virginia [94th] Choice from SF, see 1a above
4a Choice to Jacksonville for 1995 5th and 1996 6th
4b Choice from San Francisco traded to Philadelphia for 1995 5th; 1996 5th
5a Pupua, Tau DT Weber State [136th] Choice from Jacksonville, see 4a
5b Miller, Mike WR Notre Dame [147th] Choice from Philadelphia, see 4b
6 Choice to San Diego in 1994 for CB Donald Frank
7 Tellison, A.C. WR Miami [231st] Choice from NE for the Browns’ 1995 7th round selection.
Anyway the 49ers selected J.J. Stokes with the 10th pick.
(April 22-23,1995)
(Drafted 23rd)
1. (A) STOKES, J.J.
(Choice from Cleveland)
WR, 6-4, 217, UCLA
1. (B) Choice to Cleveland
2. Choice to L.A. Rams-
Pope, Marquez
3. Choice to Cleveland
4. (A) Choice to Cleveland from Kansas City-
Bono, Steve
4. (B) HANSHAW, TIM
T/G, 6-5, 300, BYU
5. Choice to Detroit-
Moore, Derrick
6. ARMSTRONG, ANTONIO
LB, 6-1, 234, Texas A&M
7. COLEMAN, HERB
DE, 6-4, 285, Trinity International