I was inspired by this thread to look up the actual roster and service time limits for the various minor leagues … here they are:
Level AAA (International, Pacific Coast): 25 man active roster, no service time limit
Levels AA (Eastern, Southern, Texas): 25 man active roster, no service time limit
Level A Advanced (California, Carolina, Florida State): 25 man active roster, 6 years service time
Level A (Midwest, South Atlantic): 25 man active roster, 5 years service time
Level A Short-Season (New York-Penn, Northwest): 35 man active roster, 4 years service time
Rookie (Appalachian, Pioneer, Arizona, Gulf Coast): 35 man active roster, 3 years service time
Rookie (Venezuelan Summer, Dominican Summer): 35 man active roster, 4 years service time
Teams in the Mexican League (which is AAA level, but has only unaffiliated teams) have essentially 30-man active rosters and 5-man reserve rosters (for a total of 35 players). No service time limits AFAIK.
Sources:
FAQs: The Business of MiLB | MiLB.com Official Info | The Official Site of Minor League Baseball (generally)
FAQs: Minor Leagues On-the-field | MiLB.com Official Info | The Official Site of Minor League Baseball (for Mexican League)