Prepare Simple Syrup: In a small saucepan, combine equal parts sugar and water, typically 1 cup each. Heat over medium heat, stirring frequently until the sugar completely dissolves, about 5 minutes. Let the simple syrup cool.

Blend Fruits: Chop 2 ripe peaches and 1 cup of pineapple. In a blender, combine the chopped fruits with 1 cup of water. Blend on high speed for about 30 seconds or until smooth.

Strain Mixture: Pour the blended fruit mixture into a fine mesh sieve over a large bowl or pitcher. Press down to extract the juice, leaving the pulp behind.

Combine Ingredients: In a pitcher, combine the strained juice with another cup of cool water and the juice of one lime. Stir in cooled simple syrup to taste.

Chill and Serve: Refrigerate the mixture for 30 minutes. Serve over ice, garnished with frozen peach slices or mint leaves.