The computation of effectiveness factors (EFs) is commonly used for simplifying heterogeneous models of catalytic processes. To do this, the reaction rate in a catalyst pellet is expressed by its rate under surface/bulk conditions multiplied by a functional factor, namely, the EF. When many EF evaluations are required, it is desirable to dispose of short-cut methods to alleviate the computational burden. Existing short-cut methods are based on the availability of analytical solutions for a related linear, but nonhomogeneous, approximation to the nonlinear kinetics. However, the nonhomogeneous term can lead to spurious solutions, such as the presence of negative concentration values. This paper proposes a derivation of the EF short-cut method as an iteration procedure in the average concentration. On the other hand, aimed at avoiding negative concentration values, the proposed linear boundary-value problem is equipped with a nonactive region. In this way, the short-cut method is composed of two nonlinear equations on the average concentration and the position of the boundary between the active and nonactive regions. Numerical results show that such a modification increases the prediction capacity of EF short-cut methods for a practically acceptable Thiele modulus region.