Jones told ESPNDallas.com on Sunday he was recovering well from a June 20 surgery, but he wouldn't specify the reason for the surgery except to say it wasn't anything life-threatening or heart-related.
"Well it's been there for quite a while," Jones, 67, said prior to Monday's practice. "Then I decided to go on and get it fixed up. A lot of things that are involved in after-surgery stuff I probably could've cut a lot shorter if I had stopped using [the arm]. You just have too much to do, so it's prolonging some of that. But it's coming along medically and certainly it's in good shape."
Jones was limited in what he could do with his right arm, including shaking hands, but recently he's been doing more of that. Before Monday's practice, he shook hands with backup quarterback Jon Kitna, who also patted him softly on the back of the shoulder.
"I kid a lot of the players sometimes about their surgeries and ask them when they think they're going to get out there full deal in a kidding way," Jones said. "Now I don't have the gall to come out here and look like I'm half-injured."
Jones has admitted he hasn't always looked or felt his best since the surgery, but things are much better nearly a month into recovery.
"Again, I'm not going to get into the details," Jones said. "But we did some serious work on cleaning some stuff."
Calvin Watkins covers the Cowboys for ESPNDallas.com. You can follow him on Twitter or leave a question for his weekly mailbag.