In this study, reaction rate sub-models are investigated in the framework of conditional moment closure (CMC) using the direct numerical simulation (DNS) database of a lifted turbulent H-2/N-2 flame. The DNS code solves the fully compressible Navier-Stokes equation system. A 9 species and 19-step mechanism for hydrogen combustion is adopted. The comparison of the DNS results and the measurements shows that, in spite of the under predicted lift-off height, the predictions of the conditional means are satisfactory. Two improved models for the conditionally averaged reaction rate are investigated a-priori. The doubly conditioned reaction rate accounts for the fluctuations with two conditioning variables while the second-order closure is based on the Taylor expansion. It is shown that both of the models give promising results. Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.