The transported PDF approach, closed at the joint composition-enthalpy level, is applied to model premixed turbulent flames at a wide range of Reynolds numbers. The initial aim of the study is to establish the impact of closure approximations for the scalar dissipation rate upon the relationship between turbulence fluctuations and predicted turbulent burning velocities. The cases considered feature stoichiometric methane-air flames with the chemical Source term extracted from a detailed chemistry simulation of the corresponding unstrained laminar flame. The transported PDF approach is subsequently combined with a systematically reduced C/H/O mechanism featuring 142 reactions and 14 solved and 15 steady-state species and applied to piloted premixed stoichiometric methane-air flames investigated experimentally by Chen et al. [Combust. Flame 107 (1996) 223-226]. The cases considered here feature Re = 24.200 (flame F3) and 52,500 (flame F1) and Damkohler numbers approaching unity. The effects of variations in the tinie-scale ratio (2 <= C-phi <= 8) and heat losses to the burner were investigated, along with the impact of an extended algebraic relationship for the scalar dissipation rate that accounts for small-scale proper-ties. Comparisons with experimental data show that the modified Curl's model and the extended scalar dissipation-rate Closure produce turbulent burning velocities in close agreement with measurements. The study further indicates that a closure at the joint scalar level combined with comprehensive chemistry has the potential to reproduce the detailed chemical structure of premixed turbulent flames. The importance of boundary conditions and comprehensive scalar statistics, including the scalar dissipation rate, is also emphasized by the study. (c) 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.