Low internal relief, aridity, and internal drainage characterize the Puna-Altiplano Plateau and the Tibetan Plateau and the Tarim basin. Structurally, these areas are reverse fault bounded terrains with intervening wedge-top basins that store thick accumulations of sediment for millions of years. Orographic barriers along the margins of these basins are oriented normal to moisture bearing winds, resulting in regional aridity. The combination of this aridity, rapid shortening and uplift rates, and resistant exposed lithologies coincides with the location of these internally drained basins. We hypothesize that these large, internally drained areas persist indefinitely when uplift overwhelms the fluvial systems and defeats the channel network. To test this hypothesis, we developed models of channel defeat to examine the threshold conditions required to fragment the channel network. The results of these models suggest that low-erodibility rocks, moderate to high uplift rates, and low precipitation favor defeat of orogen-traversing channels. Most coupled tectonic-landscape development models prevent the development of internal drainage and so may overestimate the voracity of erosion in regimes that favor internal drainage, profoundly influencing predicted orogenic growth patterns.