The internal coronagraph and the external occulter have both been proposed for imaging extrasolar planets; each has its own strengths and weaknesses. Internal coronagraphs require very accurate wavefront control, while occulters require accurate positioning and alignment, and a precisely manufactured shape. A hybrid occulter, which combines the two technologies, ideally reduces the tolerances on each, making both sytems more manufacturable. Our hybrid occulter concept combines the apodized pupil Lyot coronagraph with an external occulter. We present a number of designs which cover a wide span of suppression levels, and give a framework for creating further families of occulters with desired potential science bandwidths, occulter angular sizes, and diameters of the telescope secondary. All of these designs are capable of reaching 10 10 contrast over their entire spectrum of design. We also characterize the edge tolerances required for both systems.