Squeeze the limes, adding the pulp that you then have. Add the sugar to the measuring cup and stir vigorously. Then pour into a carafe / mug with a handle, add the mint leaves and stir. Add the rum, the well-chilled mineral water and stir everything well.
Put a few ice cubes in glasses, put a lime wedge on the edge of each glass and fill up with the mojito. Depending on the size of the glasses, it adds up to 5-10.