MySQL Cannot drop index needed in a foreign key constraint

I need to ALTER my existing database to add a column. Consequently I also want to update the UNIQUE field to encompass that new column. I'm trying to remove the current index but keep getting the error `MySQL Cannot drop index needed in a foreign key constraint` CREATE TABLE mytable_a ( ID TINYINT NOT NULL AUTO_INCREMENT PRIMARY KEY, Name VARCHAR(255) NOT NULL, UNIQUE(Name) ) ENGINE=InnoDB; CREATE TABLE mytable_b ( ID TINYINT NOT NULL AUTO_INCREMENT PRIMARY KEY, Name VARCHAR(255) NOT NULL, UNIQUE(Name) ) ENGINE=InnoDB; CREATE TABLE mytable_c ( ID TINYINT NOT NULL AUTO_INCREMENT PRIMARY KEY, Name VARCHAR(255) NOT NULL, UNIQUE(Name) ) ENGINE=InnoDB; CREATE TABLE `mytable` ( `ID` int(11) NOT NULL AUTO_INCREMENT, `AID` tinyint(5) NOT NULL, `BID` tinyint(5) NOT NULL, `CID` tinyint(5) NOT NULL, PRIMARY KEY (`ID`), UNIQUE KEY `AID` (`AID`,`BID`,`CID`), KEY `BID` (`BID`), KEY `CID` (`CID`), CONSTRAINT `mytable_ibfk_1` FOREIGN KEY (`AID`) REFERENCES `mytable_a` (`ID`) ON DELETE CASCADE, CONSTRAINT `mytable_ibfk_2` FOREIGN KEY (`BID`) REFERENCES `mytable_b` (`ID`) ON DELETE CASCADE, CONSTRAINT `mytable_ibfk_3` FOREIGN KEY (`CID`) REFERENCES `mytable_c` (`ID`) ON DELETE CASCADE ) ENGINE=InnoDB; mysql> ALTER TABLE mytable DROP INDEX AID; ERROR 1553 (HY000): Cannot drop index 'AID': needed in a foreign key constraint