Exterior wall returns affect the accuracy and fidelity of the imaged scene in urban sensing and through-the-wall radar imaging applications. For reliable imaging of stationary indoor scenes, the front wall reflections need to be properly attenuated. In this chapter, wall mitigations are addressed in the context of compressive sensing for stepped-frequency radar operation. Wall mitigation schemes, originally proposed for imaging using full data volume, maintain their proper performance with few measurements, provided that the same reduced set of frequencies is used at each available antenna position. However, having the same frequency observations across all antennas may not always be feasible. For the more challenging case when different reduced frequencies are employed at different antennas, two alternate methods based on discrete prolate spheroidal sequences (DPSS) and partial sparsity can be applied. The former captures the wall clutter energy at each antenna individually using a DPSS basis and then removes it from the reduced set of measurements. The latter considers the stationary scene reconstruction problem when the support of the image corresponding to the exterior and interior walls is known a priori.