Both players greeted the straight player-for-player transaction with good reviews. Bryant had a falling-out with Cowboys coach Bill Parcells during the spring about losing his starting job to Keyshawn Johnson without open competition. He threw a sweaty towel in the coach's face during a practice to show his anger.
Both sides put aside their differences and continued the relationship because Parcells liked the way Bryant played and his potential. Bryant started 20 games over his first two seasons but only five last year in Parcells' first year as coach. He had a 44-catch rookie season for Dave Campo and 39 catches for Parcells in his first year.
Lamont Smith, Bryant's agent, flew to Dallas on Monday to meet with the Cowboys, and he was happy with the decision to trade his client.
"Antonio was tremendously excited," Smith said. "He wants to be the main receiver in an offense, and he has a chance to take advantage of a good opportunity in Cleveland. When he was told, he said he felt it was like the night before Christmas."
Bryant, as the Cowboys' third receiver, had 16 catches for 266 yards and no touchdowns.
The meeting between the Cowboys and Bryant's agent wasn't done with the idea of requesting a trade. It was more to determine what each side thought about their futures together after the offseason incident.
"It became clear that the Cowboys weren't going to make any commitment to him in the future," Smith said. "We wanted to see how things were going to work out following what we call 'The Incident.' Both of us decided it was best to part ways."
Morgan was in a similar situation in Cleveland. He had lost playing time to Dennis Northcutt and Andre Davis, tallying nine catches for 144 yards and three touchdowns.
A second-round choice of the Browns in 2001, Morgan started 41 games in his first three seasons. He had 124 catches heading into this season.
John Clayton is a senior writer for ESPN.com.