The craft of papercutting is part of the folk art traditions of cultures all over the world. From the point of view of computer graphics, papercutting can be seen as a method of composing bi-level images under a set of geometric connectivity constraints. In this paper, we present a technique for composing digital paper-cut designs. The elements of a design may be images, which are processed via a multilayer thresholding operation, or they may be procedurallygenerated arrangements of shapes. Elements are composed using a set of boolean operators that preserve connectivity. The resulting designs are well suited to being cut by a new generation of inexpensive computer peripherals.