The Cowboys have added linebacker James Morris, who was one of three players to work out for the team following the Tuesday morning walk-through practice.
Morris, who spent some time with the Patriots and even won a Super Bowl ring for the 2014 championship season as a member of the practice squad.
The Cowboys also worked out Emmanuel Acho and Quayshawn Nealy but went with Morris, who played six games last year as a member of the Giants.
Cowboys VP Stephen Jones, the director of player personnel, said the club will likely use Wednesday's day off to evaluate more players at other positions.
Jones said the team is rather light at defensive tackle, with Tyrone Crawford sitting out with a back injury. Expect the Cowboys to bring in some tackles, along with safeties and offensive linemen.