Though Carpenter remains a member of the Bills, coach Rex Ryan called it "a possibility" the number will be down to one by Sunday, when Buffalo (2-2) travels to play Tennessee (1-2).
Cundiff is a 12-year veteran who has experience handling both kickoff and field-goal duties.
That's a combination that made Gay expendable because he failed to develop his game beyond kickoffs in two seasons in Buffalo. And it's a reason Carpenter's job security is suddenly in question.
Carpenter has been erratic since the start of the preseason while nursing assorted injuries. He has missed two of seven field-goal attempts, including a 30-yarder in a 24-10 loss to the New York Giants on Sunday. Carpenter has also missed an extra point.
"I shouldn't be really missing kicks inside 40, you know it's just as simple as that," Carpenter said.
Carpenter set the franchise record by hitting 34 field goals last season. And he had missed just seven of 72 attempts in his first two seasons in Buffalo.
Carpenter said his approach won't change because of Cundiff's arrival.
"Whether someone's here or not makes no difference," Carpenter said. "I mean, there's nothing I can do except go out there and do my best and hope they all go in."
His struggles began in the preseason when he missed three of six field-goal attempts and an extra-point try.
Cundiff is accustomed to playing in inclement conditions after spending the past two seasons in Cleveland. He was cut by the Browns after missing seven of 29 field-goal attempts, including three from within 39 yards.
Cundiff's numbers have dropped since he hit 26 of 29 attempts with Baltimore in 2010. Ever since, he's gone 78 of 104, and is on his fourth team in five years.
Moore, who doubles as a receiver, spent his first four seasons in Oakland where he had 142 catches for 2,169 yards and 17 touchdowns. He also averaged nearly 7 yards on 42 punt returns.
Moore is reunited with Bills receivers coach Sanjay Lal, who held the same job in Oakland during Moore's rookie season.