A second-order CMC model for a detailed chemical mechanism is presented and applied to turbulent piloted jet diffusion flames, Sandia Flames D, E, and E Second-order corrections are made for three rate-limiting steps of methane-air combustion, while first-order closure is employed for all the other reaction steps. The effect of a pilot flame is well predicted by the conditional scalar dissipation rate derived from a trimodal PDF for fuel, air, and pilot streams. Results show significantly improved predictions of conditional mean temperature and mass fractions of major and stable intermediate species on the fuel-rich side. Conditional mean OH and NO mass fractions are also in good agreement, although underestimated extinction seems to be responsible for overpredicted NO downstream for Flame E. Results for Flame D are in better agreement than those for Flame E which involves more significant local extinction. Second-order correction of only the chain-branching step, H + O-2 --> OH + O, is shown to capture most of the improvements by correction of the three rate-limiting steps. The predictions for Flame F do not seem to be satisfactory due to underpredicted conditional variances and covariances. Further study may be needed to clarify major causes of the deviation and to suggest possible remedies for more accurate prediction of Flame F. (C) 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.