Annular folded imagers can be up to 10× thinner than corresponding full-aperture imagers, but have tight fabrication tolerances and relatively shallow depth of focus. Wavefront coding, the use of specialized optics with postdetection signal processing, has been used to improve the depth of focus in full-aperture imaging systems. Here we explore the application of wavefront coding to annular folded optics. We compare the design and experimental results for an imaging system with a 38 mm focal length and just 5 mm total track.