Bradham served his one-game suspension for violating the league’s substance-abuse policy.
Bradham, 25, appeared in all 16 games for the Bills last season and recorded 51 tackles and a pass defense.
Smith, 24, originally signed on with the Dolphins as an undrafted free agent out of Missouri back in 2011. He later signed a future/reserve contract with the Jets before joining the Bills in October of last year.
He has yet to appear in an NFL game.