Clemons played in just six games as a reserve after being signed in November, but had a sack in his NFL debut against Pittsburgh and two more and a forced fumble over the next five games.
He played defensive end in passing situations, giving the team another option for pressuring the quarterback.
The Redskins have been courting a pass-rushing end, free agent Courtney Brown, over the last week. Brown visited the Redskins on Thursday, but also is talking with Denver and Jacksonville.
The Redskins also re-signed receiver Gari Scott, who spent last season on the practice squad, and released linebacker Maurice Jones.
Regarded as one of the top fullback prospects in several years when he was chosen by Miami in the second round of the 1999 draft, Konrad suffered a string of injuries that severely cut into his playing time and productivity. The former Syracuse standout has played in all 16 games only once and has never started more than 14 games in a season. In 2004, he started just one game and logged only 10 "touches" all season.
Konrad, 28, will be reunited in Oakland with Raiders head coach Norv Turner, who was offensive coordinator in Miami for part of the fullback's tenure there. The New York Giants also had an interest in Konrad.
In six seasons, Konrad has 38 carries for 114 yards and one touchdown. He also has 111 catches for 854 yards and six touchdowns.
Cook, 25, started the final six games for the Cleveland Browns last season. He was waived Nov. 17 by Baltimore after playing in the Ravens' first nine games of 2004.
Cook also has spent time with the Chicago Bears, and was on the Dolphins' practice squad in 2003.
Cincinnati Bengals: Unrestricted free agent safety Anthony Mitchell, a career backup but strong special teams player, has agreed to re-sign with the Bengals. A five-year veteran, Mitchell will sign a one-year contract believed to include a minimum base salary of $540,000.
Mitchell, 30, signed with the Bengals a month into the 2004 season, after the Jacksonville Jaguars released him. Head coach Marvin Lewis was familiar with Mitchell from their time together with the Baltimore Ravens. In 12 games last season, Mitchell backed up at both safety spots and posted 16 special teams tackles, third-most on the club.
The former Tuskegee standout has played in 76 games, and started seven of them, in stints with Baltimore (2000-2002), Jacksonville (2003) and Cincinnati (2004). He has five tackles from scrimmage, three interceptions, three passes defensed and one fumble recovery.
Senior NFL writer Len Pasquarelli and The Associated Press contributed to this report.