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It is generally supposed that when the "compactness" $l \equiv L\sigma_T/(rm_e c^3)$ in photons above the pair-production threshold is large, few$\gamma$-rays can escape. We demonstrate that even when $l \gg 1$, if the highenergy and low energy photons are produced in geometrically-separated regions,many of the $\gamma$-rays can, in fact, escape. Pair-production along a thinsurface separating the two sources creates enough Compton optical depth todeflect most of the low energy photons away from the high energy ones. Thosefew low-energy photons which penetrate the shielding surface are reduced inopacity by advection to large distance and small density, by relativisticbeaming along the inner edge of the surface, and by Compton upscattering tohigher energies inside the surface. The pairs in this surface flow outwardrelativistically, forming a structure resembling a pair-dominated mildlyrelativistic jet.Comment: 20 pages, 3 figures, AAS LaTeX, in press Ap.

Self-Shielding of X-Rays and Gamma Rays in Compact Sources