When bringing animated characters to life, artists often augment the primary motion of a figure by adding secondary animation - subtle movement of parts like hair, foliage or cloth that complements and emphasizes the primary motion. Traditionally, artists add secondary motion to animated illustrations only through arduous manual effort, and often eschew it entirely. Emerging "live" performance applications allow both novices and experts to perform the primary motion of a character, but only a virtuoso performer could manage the degrees of freedom needed to specify both primary and secondary motion together. This paper introduces physically-inspired rigs that propagate the primary motion of layered, illustrated characters to produce plausible secondary motion. These composable elements are rigged and controlled via a small number of parameters to produce an expressive range of effects. Our approach supports a variety of the most common secondary effects, which we demonstrate with an assortment of characters of varying complexity.