Fields' new deal is worth $13 million and includes $3.3 million in guaranteed money. Fields was scheduled to become a free agent after the 2012 season, but he's now signed through 2016.
Carpenter and Denney, the longest-tenured member on the team, are signed through 2013.
The Dolphins have good reason to hang on to Fields, who has done nothing but get better since arriving in 2007 as a seventh-round pick out of Michigan State.
Fields set single-season franchise records in gross (48.8) and net (41.4) averages in 2011, and ranked third in the league in gross average behind only the 49ers' Andy Lee and the Raiders' Shane Lechler.
Fields and Denney are two of only three players who have been with the team since 2007, the other being fellow 2007 draft pick Paul Soliai.
Even with Fields' extension, the Dolphins still have 24 players scheduled to become unrestricted free agents next spring. Leading the list are tackle Jake Long, running back Reggie Bush, wide receiver Chad Johnson, defensive tackle Randy Starks, and quarterbacks Matt Moore and David Garrard.