Stir water and sugar in heavy medium saucepan
over high heat until sugar dissolves
and syrup comes to boil.
Remove from heat and cool.
Puree Strawberries in processor or blender.
Strain into medium bowl.
Mix 1/4 cup rum, lime juice, triple sec
and syrup into puree. Chill until cold.
Process mixture in ice cream maker
according to manufacturer's instructions.
Transfer to container; cover tightly.
Freeze until firm. Makes 6 Cups