Swirling-sweepers is a new method for modeling shapes while preserving volume. The artist describes a deformation by dragging a point along a path. The method is independent of the geometric representation of the shape. It preserves volume and avoids self-intersections, both local and global. It is capable of unlimited stretching and the deformation can be constrained to affect only a part of the model.We argue that all of these properties are necessary for interactive modeling if the user is to have the impression that he or she is shaping a real material. Our method is the first to implement all five.