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Add sugar, mint sprigs and 1 cup of water to a small saucepan over medium heat and bring to a simmer. Simmer until the sugar dissolves completely, remove from heat and set aside.
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Cool syrup to room temperature and discard the mint sprigs.
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In a pitcher combine: lemon juice, simple syrup, and cold water stir well. Add first two cups of water, taste, and if the mixture is too sweet add more water, making it as diluted as you prefer.
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Add the sliced lemon and to the pitcher, refrigerate for 30-60 minutes.
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Serve with ice, lemon slices, and fresh mint leaves if desired.