Maynard has played in 223 career regular season games. He was originally selected by the New York Giants in the third round of 1997 draft, and played for New York through the 2000 season. Following his stint with the Giants, Maynard played for the Chicago Bears from 2001 through last season.
He has 1,258 career punts for 52,739 yards with a gross average of 41.9 yards and has placed 407 punts inside the 20-yard line. In 2008, he led the NFL with 40 punts inside the 20.
Maynard spent training camp with the Houston Texans before being released on September 3.
McGee punted eight times in the Browns' Week 1 loss to Cincinnati for an average of just 36 yards, with the poor performance resulting from an apparent back injury.