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We simulate the performance of a gravitational wave interferometer in the Dual Recycling (DR) configuration, as will be used for systems like Advanced-LIGO. Our grid-based simulation program models complex interferometric detectors with realistic optical deformations (e.g., fine-scale mirror surface roughness). Broadband and Tuned DR are modeled here; the results are also applied qualitatively to Resonant Sideband Extraction (RSE). Several beneficial properties anticipated for DR detectors are investigated: signal response tuning and narrowbanding, power loss reduction, and the reclamation of lost power as useful light for signal detection. It is shown that these benefits would be limited by large scattering losses in large (multi-kilometer) systems. Furthermore, losses may be resonantly enhanced (particularly for RSE), if the interferometer's modal resonance conditions are not well chosen. We therefore make two principal recommendations for DR/RSE interferometers: the DR/RSE cavity must be modally nondegenerate; and fabricated mirror surfaces and coatings must be as smooth as is practically feasible.