Bring limes to room temperature.

Roll limes firmly against the counter to soften their rinds.

Halve and juice the limes, reserving the juice.

Cut lime rinds into 1-inch chunks.

Toss lime rinds with sugar in a large nonreactive mixing bowl.

Cover the bowl tightly with plastic wrap.

Let stand at room temperature, stirring every 45 minutes, until sugar dissolves (about 3 hours, or up to 12 hours).

Add water and 6 ounces of reserved lime juice.

Stir well.

Strain the mixture through a fine-mesh strainer or cheesecloth into a glass or ceramic container.

Refrigerate the concentrated limeade for up to 1 week.

To serve, pour limeade over ice.

Adjust to taste with additional water or lime juice.