All three players were reserves last season, but Bush and Olsen saw substantial playing time.
Bush appeared in all 16 games and led the Saints with 15 special teams tackles to go with a fumble recovery. He also had an interception, which he returned 40 yards, to go with 13 tackles on defense.
The 6-foot-3, 305-pound Olsen also appeared in 16 games last season, often checking in as a tackle-eligible tight end, giving the Saints an extra blocker.
Higgins was signed by New Orleans as an undrafted free agent in 2011. The 6-6 tight end has appeared in four games with one start.
Copyright 2013 by The Associated Press