An algorithm was developed to generate simplified (skeletal) mechanisms, from a given detailed one, able to replicate the dynamics of a user-specified set of species (chosen from the original set) to within a user-specified error tolerance when a finite set of sampling points, U, in the chemistry configuration space is given. The simplification procedure involves discarding elementary reactions and species that are deemed unimportant in the set U. The criteria used in deciding which elementary reactions or species to discard are based on the Computational Singular Perturbation (CSP) method. The procedure involves applying the CSP analysis to each point in U and an algorithm to assemble the simplified mechanism that is valid for all the points in U and is optimized for the set of scalars specified. This algorithm provides a convenient way to construct comprehensive simplified mechanisms, applicable over a wide range of parameters and combustion processes. The effectiveness of this new algorithm is demonstrated by constructing simplified mechanisms that are optimized for two reactive flow systems-namely a perfectly stirred reactor and a premixed flame of methane and air.