The Bills will carry both Carpenter and Cundiff on their 53-man roster for the immediate future, although coach Rex Ryan said Wednesday that it's possible the team will keep only one of the two kickers for Sunday's game against the Tennessee Titans.
Asked which kicker would handle field goals in Tennessee, Ryan said, "We'll see how the week goes."
The Bills listed Carpenter with a left knee injury last week but Ryan said Wednesday that Carpenter is "fine."
To make room for Cundiff, the Bills waived kicker Jordan Gay, who had handled kickoffs in place of Carpenter since the start of the 2014 season.
"Sometimes just carrying a kickoff guy, sometimes isn't the best thing for your team," Ryan said. "But this move had nothing to do with Jordan. I think Jordan did a tremendous job in the role that he had."
In addition to Cundiff, the Bills also signed veteran wide receiver Denarius Moore. The fifth-year receiver, who has 142 catches in 51 career games, adds depth at a position where the Bills could be without Sammy Watkins (calf) for Sunday's game.
Moore will handle punt returns for Sunday's game after the Bills waived return specialist Marcus Thigpen on Wednesday.
Asked after Sunday's game about Carpenter's missed field goal, Ryan said, "We'll look at everything right now. We got to get better, we know that."
However, Ryan backed off when asked about Carpenter's miss Monday.
"Dan knows -- I mean, shoot -- you got to make a 30-yard field goal," Ryan said. "Now he is also a pro. He also hit a 51-yarder. So we will see how it goes. I know there is nobody [that] feels worse than he does. I mean, he is trying his best.
"You guys have been around him a lot longer than I have. He is competitive, he wants it in the worst way to make kicks, but for some reason he has had a couple misses."
Carpenter missed three field goals and an extra point in the preseason. He has converted five of his seven field goal attempts in the regular season and missed an extra-point attempt in a Week 2 loss to the New England Patriots.
Cundiff worked out for the Bills on Sept. 7 following Carpenter's preseason struggles.