IRVING, Texas -- The first phone call came around noon on Thursday, and the Cowboys were quite surprised to hear the St. Louis Rams were willing to move down in the first round.

There was only one player owner/general manager Jerry Jones wanted to move up to get, and that was LSU cornerback Morris Claiborne. He was the second-highest rated player on the draft board behind Andrew Luck, who was going to the Indianapolis Colts.

Jones said the scouts told him Claiborne was the highest-rated corner on their draft boards since Deion Sanders.

"Deion had the highest touchdown-per-touch of any player in NFL history," Jones said.

The Cowboys hadn't spent much time with Claiborne during predraft workouts because, as executive vice president Stephen Jones said Thursday night, they "didn't think it was realistic" the team would be able to draft him from the No. 14 position.

Only assistant secondary coach Joe Baker and a few scouts had spoken to Claiborne. Baker talked to Claiborne at the scouting combine in Indianapolis.

But as the draft started Thursday night, the Rams called again. And this time the move was made. The Rams offered the sixth overall pick and asked for the Cowboys' 14th overall pick and their second-round selection (45th overall) to make the deal.

Stephen Jones was surprised at what was being offered.

Under one draft trade chart, normally a team would give up not only a second-round pick, but a fourth-round pick, as well, to move up from 14 to 6.

But St. Louis didn't ask for that much, and after about a four minute conversation, the Cowboys agreed to the deal.

"We didn't know for sure they would do the trade," Stephen Jones said. "All the trades are contingent on getting done when you get on the clock and agreeing to everything."

St. Louis took LSU defensive tackle Michael Brockers with the 14th pick.

The Rams, coming off a 2-14 season, are in a rebuilding process and trying to accumulate as many draft picks as possible. So, on Day 2 of the draft, the Rams have the first and 13th picks of the second round. In Round 3, the Rams have the second pick.

The Cowboys have just one pick, the 19th pick (81st overall) in Round 3.

"No one values a pick more than I do," Stephen Jones said. "It makes me sick we don't have the second pick, but if you're going to get an elite player from the 14th hole in the draft it's going to cost you something."