This year teams such as Monmouth, St. Mary's, St. Bonaventure, South Carolina and Valparaiso.
But it's also a second chance for some pretty good teams that just missed stealing a big-tournament bid.
Teams such as Long Beach State, which missed what might have been a game-winning three-pointer at the buzzer of the Big West Conference tournament championship against Hawaii.
The 49ers (20-14) will open NIT play Tuesday at Washington (18-14).
In other games Tuesday, High Point (21-10) is at South Carolina (24-8), Davidson (20-12) is at Florida State (19-13), Alabama (18-14) is at Creighton (18-14), Florida (19-14) is at North Florida (22-11), Texas Southern (18-14) is at Valparaiso (26-6), Indiana Purdue Fort Wayne (24-9) is at San Diego State (25-9), and New Mexico State (23-10) is at St. Mary's (27-5).
First-round games Wednesday are Akron (26-8) at Ohio State (20-13), Wagner (22-10) at St. Bonaventure (22-8), Belmont (20-11) at Georgia (19-13), Bucknell (17-13) at Monmouth (27-7), Hofstra (24-9) at George Washington (23-10), Princeton (22-6) at Virginia Tech (19-14), Houston (22-9) at Georgia Tech (19-14), and Alabama Birmingham (26-6) at Brigham Young (23-10).