<p>This investigation highlights an important application of complete geometric decoupling in constructing anisotropic, compact density-matter stars via a decoupled gravitational framework. In this context, the present study introduces an intriguing synthesis of two independent techniques, density-like constraints and the zero-complexity factor, to simultaneously derive the decoupler functions. By using this innovative relativistic scheme, we gain the ability to analytically control the anisotropies and complexity when modeling the dense-matter compact stars. We show that the complexity-free condition effectively captures the influence of anisotropic pressure inherent in compact dense-matter distributions, arising naturally from the chosen seed metric ansatz. Two distinct and physically viable anisotropic models satisfying all standard stability and energy conditions are obtained through the complete decoupling process. Our findings provide clear theoretical understanding of the coupling between known and standard gravity fields by demonstrating for the first time that the parameter responsible for deformation uniquely governs the direction of energy transfer between the seed sector and the decoupling source.</p>