Peel and segment the grapefruits with a knife. Remove the seeds and the white pith. In a saucepan, combine the water, sugar, and about half the peel from one of the red grapefruits. Bring to a boil over medium-high heat, stirring to dissolve the sugar.

Add the grapefruit, reduce heat to low, and simmer for 25 minutes, or until the segments have softened but still hold their shape.

Remove from the heat and discard the peel. Stir in the Cointreau, then let the grapefruit segments cool to room temperature in their syrup.

Cover and refrigerate for 24 hours. Divide among dessert bowls, garnish each with a mint sprig, and serve.