Martha's Extra-Lemony Lemonade

Juice halved lemons (you should have about 1 1/2 cups). In a small saucepan, bring sugar and 1 1/2 cups water to a simmer, stirring until sugar is dissolved. Add lemon rinds; cook over medium until mixture is syrupy, about 12 minutes. Strain; let cool completely.

Muddle mint with syrup in a pitcher. Stir in juice and 4 cups cold water. Top with ice and lemon slices; serve.