An efficient formulation of computational singular perturbation (CSP) is proposed for toy problems that consist of three variables. The essence of the new CSP formulation is to take advantage of short species time-scales that can be analytically derived or efficiently evaluated through numerical computations. Complication induced by the presence of partial equilibrium reactions is discussed. It is shown that linear combinations of fast variables may result in slow modes. Special analytic treatments are proposed for the toy problems, and such treatments may be extended for general stiff chemistry in future study. This work demonstrates the possibility of efficient analytic or semianalytic approaches to enable on-the-fly chemical stiffness removal using CSP. In contrast, the previous CSP methods involve expensive eigen-computation and are typically expensive for large-scale combustion simulations.