Lake Constace or Lake of Constance ( German : Bodensee ) is a large Lake on the river Rhine . Lake Constance ( German : Bodensee ) is a lake on the Rhine at the northern foot of the Alps , and consists of three bodies of water : the Obersee ( `` upper lake '' ) , the Untersee ( `` lower lake '' ) , and a connecting stretch of the Rhine , called the Seerhein .