This used to always confuse me too. I finally found something that explains it. The minor league portion has two phases - AAA phase and AA phase. For the AAA phase, the player has to be AA or below, and the new club is required to keep him on the AAA reserve roster (but not necessarily on the AAA active roster) the entire season, or he goes back. For the AA phase, the player has to be A or below, with the same roster requirements (has to be on the AA reserve roster the entire season). That makes it slightly different than the major league phase, as players taken in that have to stay on the active roster all year and not just the reserve roster. For AAA teams the reserve roster can have up to 38 players; AA can have up to 37 players; A and below can have up to 35 players. For the major leagues, of course, the reserve roster is the 40-man roster.