The Bengals have agreed to a two-year deal with running back Cedric Peerman, a special teams standout who could have become a free agent next week.
Peerman had two long runs off fake punts last season. He also carried 34 times for 178 yards.
Also on Thursday, the Bengals made tender offers to safety Jeromy Miles, receiver Andrew Hawkins and linebacker Vincent Rey, all of whom have contracts that expire on Monday.
As a result of the offers, Miles will become a restricted free agent next week. The Bengals maintained exclusive rights to Hawkins and Rey for next season.