In simulating chemically reacting flows, the differential entropy inequality (the local form of the second law of thermodynamics) must be satisfied in addition to the differential mass, momentum, and energy balances. Previously, we have shown that entropy violations occur when using a global/reduced mechanism. Herein we show that entropy violations also occur when using a detailed/skeletal/reduced mechanism. Using a recent theorem of Slattery et al. (2011, Role of Differential Entropy Inequality in Chemically Reacting Flows, Chem. Eng. Sci., 66(21), pp. 52365243), we illustrate how to modify a reduced chemical kinetics model to automatically satisfy the differential entropy inequality. The numerical solution of a methane laminar flame was improved when using reduced chemical kinetics modified in this way. In addition, an ad hoc temperature limiter is no longer necessary.