The assumption of reflection symmetry is one of the major deficiencies for the model based decompositions. The introduction of helix scattering components can mitigate some of the impact of this assumption, while simultaneously generating some new negative power problems. The helix mechanism has been developed in the Krogager coherent target decomposition, where there is no negative power problem. Why do these problems happen in the model based decompositions? In this paper, we review the Krogager decomposition based on the coherency matrix form of the unified CTD model, and come to the conclusion that the imaginary of is an overestimate of the helix contribution, which is the main cause of the problem. Furthermore, we review the techniques of symmetric scatterer transformation in the Cameron and Huynen decompositions, and expand them to the multi-look coherency matrix. Two new models of the nonlinear programming problem are proposed to get the transformed coherency matrix: 1) by subtracting the asymmetric component, and 2) by the procedure of con-diagonalization. A new parameter is established to measure the degree of reflection asymmetry of the coherency matrices. Experimental results in the L-band AIRSAR San Francisco data show that the two new models can reduce the correlations between co-polarized and cross-polarized channels significantly. In this case, the assumption of reflection symmetry is reasonable for the transformed coherency matrices, and negative power problems related to helix scattering no longer exist in the model based decompositions, hence the helix scattering component is not needed. Lastly, the FDD has been applied to the transformed coherency matrices. Experimental results showed that the decomposition results can reflect the predominant characteristics of the ground objects.