In blender, place limeade, rum, water, and sugar. Blend well and then stir in lemon-lime beverage. Place in freezer. Mixture will not freeze completely, but will be more like a slush. To serve: Remove from freezer, place in glasses and add garnish such as lime, mint leaf, etc.
Note: To make strawberry daiquiri, add frozen strawberries and place in blender with other ingredients.