Orientation angle compensation has been incorporated into model-based decomposition to cure the overestimation of volume scattering contribution, by rotating the coherency matrix to minimize the cross-polarization term. However, this processing cannot always guarantee to rotate the double- and odd-bounce scattering components back to zero orientation angle cases and with zero cross-polarization power. Therefore, built-up patches with large orientation angles may still suffer from the scattering mechanism ambiguity. In this paper, general double- and odd-bounce scattering models are proposed to fit for the cross-polarization and off-diagonal terms, by separating their independent orientation angles. The general decomposition framework is proposed and utilizes the complete information. The residual minimization criterion is used for model inversion. The optimal solutions are obtained using the nonlinear least square optimization technique. The manual interference and negative power issues are well avoided during the model inversion. Its efficiency and advantages are demonstrated and evaluated with airborne Xband Pi-SAR polarimetric SAR datasets. Comparison studies are also carried out. Further improved decomposition performance is achieved by the proposed method, especially in oriented built-up areas.