In a large saucepan, bring the berries, water, and sugar to a boil over medium-high heat. Turn the heat down and simmer uncovered for about 10 minutes, stirring occasionally. Pour the berry mixture through a fine-mesh strainer into a gallon-size pitcher, pressing the berries with the back of a spoon to squeeze out every last drop of juice. Discard all that’s left in the strainer.

Add the iced tea to the pitcher and stir. Refrigerate the tea for at least 1 hour before serving. Add additional berries and lemon rounds to the pitcher, then pour over ice.

Garnish with a wedge of lemon, a few berries, and a mint sprig, if desired.