It took them nearly three decades to pull it off, but the Browns are hoping they get similar results.
In 1985, the Browns took part in the NFL's supplemental draft and struck gold with the selection of Bernie Kosar.
On Thursday, the Browns took part in this year's supplemental draft, nearly 27 years later than the last time they did so. They selected wide receiver Josh Gordon in the second-round. Kosar was taken in the first round.
"I am extremely excited to have the opportunity to become part of such a prestigious organization as the Cleveland Browns," Gordon said after the selection. "I can't wait to get started and acclimated to a new city as well as the team.
"I have also had the chance to speak with Coach (Pat) Shurmur on several occasions and I am looking forward to the opportunity to play for him," he said. "Being taken this high in the supplemental draft and mentioned among the likes of the Bernie Kosar is a humbling experience in itself, as well as a dream come true."
The Browns will forfeit their second-round pick in the 2013 NFL Draft with the selection of Gordon, who last played at Baylor in 2010 where he led the team in touchdowns with seven teaming up with Robert Griffin III.
After being dismissed from Baylor, he transferred to Utah where he sat out the 2011 season under the NCAA transfer rule.
Heckert feels Gordon could be similar to Greg Little, whom the Browns took in the second-round of the 2011 draft after he sat out a season at North Carolina. He caught 61 passes to lead the Browns last year as a rookie.
"First and foremost we think the guy is a good player, but if he wasn't available it wasn't a big deal," Heckert said. "We just think he is a good player. As you said, we did look at the guys who are supposedly coming out in the draft next year and kind of compared Josh to those guys, which you have to do. Where we got Josh, I think it was good value and we got him a year early."
Heckert said one difference between Little and Gordon is that Gordon was able to practice with the Utah football team last year, even though he couldn't play in games. Little was not allowed to practice with the Tar Heels in his final season.
Gordon thinks he can contribute this season.
"I want to be able to contribute to the offense in any way I can, and I am ready to come in and work hard to make that happen."
Obviously, Heckert thinks he can contribute right away to give up a second-round draft choice.
"We hope he comes in and plays right away, that's the goal."