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In this letter, we develop several new aspects of target decomposition theory for use with compact-mode polarimetric radar data. We first make a general link between fully polarimetric systems and compact modes before developing two important types of decomposition, namely, entropy/alpha and model-based surface/dihedral/volume techniques. We show that, under certain assumptions, compact data can be used to estimate the rotation invariant alpha angle of quadpol systems, which can then be used for polarimetric classification and physical parameter estimation. We apply the new methods to the problem of historical forest fire scar detection, using data at L- and C-bands to demonstrate the preservation of signatures in transition from quad to compact modes.