To make a simple syrup, combine sugar and ½ cup water in a small pot. Bring to a boil. Stir, and reduce heat to medium high. Stir occasionally until sugar is dissolved, approximately 5 minutes. Let the simple syrup cool.
Finely chop the mint.
Add the mint, 4 cups of water, lemon juice, and ¼ cup of the simple syrup to a pitcher. Stir well, and chill.
Filter out the mint leaves before serving.
Garnish with a stem of mint.
Garnish with lemon slices.
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