The moves leave the Dolphins with 51 players on the active roster, two under the limit.
The big move was the one involving the wide receivers.
Naanee was cut two days after he fumbled the ball — untouched — after catching a pass in the fourth quarter of Sunday's 24-21 overtime loss at Arizona. Mind you, it was Naanee's first reception of the season.
Signed as a free agent after catching a career-high 44 passes for Carolina last season, Naanee's failure to produce was one of the biggest reasons the Dolphins wide receiver corps has been a trouble area since the start of camp.
Gaffney, a 10-year veteran who has played with four teams, was released by New England this summer after battling a variety of injuries. He worked out for the Dolphins several weeks ago.
Like Naanee, he's also coming off the most productive season of his career after catching 68 passes for 947 yards and five touchdowns for Washington in 2011.
Gaffney, who has also played for Houston, New England and Denver, isn't particularly fast, but he's a good route-runner and can make the tough catch.