We recently described a technique called basis pursuit dictionary editing (BDPE) that uses L1 minimization techniques to remove contamination from ISAR measurements and imagery of rotating targets [1]. While our original BPDE technique works well when the target scattering is dominated by literal (non-interacting) returns, non-literal target scattering, such as the returns from re-entrant cavities, can “leak” into the contamination bases and be discarded in the editing process. In this paper, we extend the BPDE technique to include a simple and efficient basis for the scattering from re-entrant cavities on the target, and demonstrate its effectiveness in separating those returns from the literal target scattering using numerical simulations. We also describe how the basis can be easily generalized to near field ISAR measurements.