Computations of turbulent combustion flows using detailed chemistry involving a large number of species and reactions are computationally prohibitive, even on a distributed computing system. Here, we present a new combined dimension reduction and tabulation methodology for the efficient implementation of combustion chemistry. In this study, the dimension reduction is performed using the rate controlled constrained-equilibrium (RCCE) method, and tabulation of the reduced space is performed using the in situ adaptive tabulation (ISAT) algorithm. The dimension reduction using RCCE is performed by specifying a set of represented (constrained) species, which in this study is selected using a new Greedy Algorithm with Local Improvement (GALI) (based on the greedy algorithm). This combined approach is found to be particularly fruitful in the probability density function (PDF) approach, wherein the chemical composition is represented by a large number of particles in the solution domain. In this work, the combined approach has been tested and compared to reduced and skeletal mechanisms using a partially-stirred reactor (PaSR) for premixed combustion of (i) methane/air (using the 31-species GRI-Mech 1.2 detailed mechanism and the 16-species ARM1 reduced mechanism) and (ii) ethylene/air (using the 111-species USC-Mech II detailed mechanism, a 38-species skeletal mechanism and a 24-species reduced mechanism). Results are presented to quantify the relative accuracy and efficiency of three different ways of representing the chemistry: (i) ISAT alone (with a detailed mechanism); (ii) ISAT (with a reduced or skeletal mechanism); and (iii) ISAT-RCCE with represented species selected using GALI. We show for methane/air: ISAT (with ARM1 reduced mechanism) incurs 6% error, while ISAT-RCCE incurs the same error using just 8 or more represented species, and less than 1% error using 11 or more represented species, with a twofold speedup relative to using ISAT alone with the GRI-Mech 1.2 detailed mechanism. And we show for ethylene/air: ISAT incurs 7% and 3% errors with the reduced and skeletal mechanisms, respectively, while ISAT-RCCE achieves the same levels of error 7% with just 18 and 3% with just 25 represented species, and also provides 15-fold speedup relative to using ISAT alone with the USC-Mech II detailed mechanism. With fewer species to track in the CFD code, this combined ISAT-RCCE-GALI reduction-tabulation algorithm provides an accurate and efficient way to represent combustion chemistry. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.