The rate-controlled constrained equilibrium (RCCE) is a model reduction scheme for chemical kinetics. It describes the evolution of a complex chemical system with acceptable accuracy with a number of rate controlling constraints on the associated constrained-equilibrium states of the system, much lower than the number of species in the underlying detailed kinetic model (DKM). Successful approximation of the constrained-equilibrium states requires accurate identification of the constraints. One promising procedure is the fully automatable Approximate Singular Value Decomposition of the Actual Degrees of Disequilibrium (ASVDADD) method that is capable of identifying the best constraints for a given range of thermodynamic conditions and a required level of approximation. ASVDADD is based on simple algebraic analysis of the results of the underlying DKM simulation and is focused on the behavior of the degrees of disequilibrium (DoD) of the individual chemical reactions. In this paper, we introduce an alternative ASVDADD algorithm. Unlike the original ASVDADD algorithm that require the direct computation of the DKM-derived DoDs and the identification of the set of linearly independent reactions, in the alternative algorithm, the components of the overall degree of disequilibrium vector can be computed directly by casting the DKM as an RCCE simulation considering a set of linearly independent constraints equaling the number of chemical species in size. The effectiveness and robustness of the derived constraints from the alternative procedure is examined in hydrogen/oxygen and methane/oxygen ignition delay simulations and the results are compared with those obtained from DKM.