A 3D binary digital image is said to be <i>well-composed</i> if and only if the set of points in the faces shared by the voxels of foreground and background points of the image is a 2D manifold. Well-composed images enjoy important topological and geometric properties; in particular, there is only one type of connected component in any well-composed image, as 6-, 14-, 18-, and 26-connected components are equal. This implies that several algorithms used in computer vision, computer graphics, and image processing become simpler. For example, thinning algorithms do not suffer from the irreducible thickness problem if the image is well-composed, and the extraction of isosurfaces from well-composed images using the Marching Cubes (MC) algorithm or some of its enhanced variations can be simplified, as only six out of the fourteen canonical cases of cube-isosurface intersection can occur. In this paper, we introduce a new randomized algorithm for making 3D binary digital images that are not well-composed into well-composed ones. We also analyze the complexity and convergence of our algorithm, and present experimental evidence of its effectiveness when faced with practical medical imaging data.