Other Exceptions for players NOT related to the Larry Bird situation:
Mid-Level Exception
Once every season each team can use the mid-level exception to sign a player. The contract amount and duration depend on the teams status in the salary cap.
To simplify , any team without cap room but which is below the tax apron (not in luxury tax) can sign a player for $5.3 million; a team over the luxury tax can sign a player for $3.2 million and a team with cap room can sign a player to an mid-level exception for $2.5million (teams under the cap were previously unable to sign players on an mid-level exception).
Why would a team under the cap wish to do so? If they plan multiple transactions, this gives a team a better strategy by which they can claim which transaction (not necessarily chronological) it places under the exception.
Bi-Annual Exception
The Bi-Annual exception allows teams to sign players for contracts starting at $1.6 million for the first year, with a maximum of an 8% raise for the following year. Teams already in the luxury tax are not allowed to sign players through this exception as many were using it to sign top paid players.
Rookie Exception
The Rookie Exception allows players to sign their draft choices to rookie scale contracts even if it means they would push them over the cap limit.
Next: Unique Circumstance Exceptions