In a saucepan combine ¾ cup of water with the sugar, lemon juice, and lemon peel (and rum or vanilla extract if desired). Bring to a boil, then reduce the heat and add the fruit. Cook at a very low heat for 5 minutes.
Pour the syrup into a cup and set aside. Remove the lemon peel and cool the cooked fruit for 2 hours.
To serve the compote, arrange the fruit in a serving dish and pour a few teaspoons of syrup over the fruit. Garnish with mint leaves (if desired).