Last season, 59 undrafted rookie free agents made Week 1 rosters, including Justin Tucker, the kicker for the Super Bowl champion Baltimore Ravens. If that's not enough convincing on importance of the priority free agents, then consider that there are 15 members of the Pro Football Hall of Fame who went undrafted.
These players still have a chance of finding the right situation to succeed:
1. Tyler Bray, QB, Tennessee -- Bray came out of school early to pursue a career in the NFL. He had better success at the end of the 2012 season than at the beginning, and displayed probably the strongest arms of any quarterback in this year's draft class. (UPDATE: Bray reportedly has signed with the Kansas City Chiefs.)
2. Jeff Tuel, QB, Washington State -- Mike Leach, the coach at Washington State, called me about a week ago and said that he thought Tuel had a real good chance of developing into an NFL starting quarterback in time. Tuel is a developmental prospect with the ability to be an eventual starter in the right situation. (UPDATE: Tuel has signed with the Bills, the Buffalo News reported.
3. LaAdrian Waddle, OT, Texas Tech -- He has height and long arms, which are needed to play offensive tackle in the NFL, but he's probably only a right tackle as a pro. (UPDATE: Waddle has signed with the Detroit Lions, according to MLive.com.)
4. Ryan Otten, TE, San Jose State -- I think he was overlooked. Otten has a chance to be a starter in the NFL. (UPDATE: Otten has signed with the Jacksonville Jaguars, according to draftinsider.net.
5. Matt Scott, QB, Arizona -- Coach Rich Rodriguez described Scott as the best quarterback prospect he's coached in 23 years. This is a very athletic quarterback. (UPDATE: Scott has signed with the Jaguars, according to CBSSports.com.)
6. Robert Lester, FS, Alabama -- Lester was a three-year starter for coach Nick Saban at Alabama. That's saying something. To be a starter for Saban for that long means Lester has been taught real well. (UPDATE: Lester reportedly is bound for the Carolina Panthers.)
7. Cory Grissom, DT, South Florida -- Grissom is a very active player with the measurables you want in an NFL defensive end. (UPDATE: Grissom has signed with the New England Patritos, according to the Tampa Bay Times.)
8. Emmett Cleary, OT, Boston College -- Cleary played left tackle at Boston College, but he might not be able to do that in the NFL. He is a big, long-armed player whose best spot might be right tackle.
9. Chase Thomas, OLB, Stanford -- Thomas doesn't have great speed, but is a very active, smart player who has great recognition. (UPDATE: Thomas tweeted Saturday that he's joining the New Orleans Saints.)
10. Kwame Geathers, NT, Georgia -- The history in the game of the Geathers family means Kwame has the pedigree to perform in the pros. (UPDATE: Geathers has signed with the San Diego Chargers, according to UT-San Diego.)
Follow Gil Brandt on Twitter @Gil_Brandt.