Jones, a 2013 seventh-round draft choice out of Arkansas State, played in 16 games last season for Miami. His primary contributions came on special teams as a gunner and led the club with 11 special teams tackles last year.
The 5-foot-11, 205-pound Jones joins a deep safety corps in New England that includes Devin McCourty, Patrick Chung, Duron Harmon. Tavon Wilson and Nate Ebner. It's one of the few positions where the Patriots figured to be seeking depth.
One line of thinking is that the Patriots could potentially receive some Dolphins-based intelligence from Jones leading into the Sept. 7 season opener between the teams. Jones made headlines in May, and earned a suspension from the Dolphins, for his tweets on Michael Sam's reaction to being drafted.
As for Barker, the Patriots have groomed him over the past year after claiming him on waivers from Miami at the final cutdown last year. Barker, a guard who also played left tackle in training camp and preseason, would almost certainly sign to the team's practice squad if he clears waivers.
The Patriots kept 10 offensive linemen on their initial 53-man roster, which is a bit higher than the league average.