Lean premixed combustion is at present one of the most promising methods to reduce emissions and to maintain high efficiency in combustion systems. As the emission legislation becomes more stringent, modelling of turbulent premixed combustion has become an important tool for designing efficient and environmentally friendlier combustion systems. However, in order to predict these emissions reliable predictive models are required. One of the methods used for predicting pollutants is the conditional moment closure (CMC), which is suitable to predict pollutants with slow time scales. Despite the fact that CMC has been successfully applied to various non-premixed combustion systems, its application to premixed flames is not fully tested and validated. The main difficulty is associated with the modelling of the conditional scalar dissipation rate (CSDR) of the conditioning scalar, the progress variable. In premixed CMC, this term is an important quantity and represents the rate of mixing at small scales of relevance for combustion. The numerical accuracy of the CMC method depends on the accuracy of the CSDR model. In this study, two different models for CSDR, an algebraic model and an inverse problem model, are validated using two different DNS data sets. The algebraic model along with standard k-ε turbulence modelling is used in the computations of stoichiometric and very lean pilot stabilized Bunsen flames using the RANS-CMC method. A first order closure is used for the conditional mean reaction rate. The computed nonreacting and reacting scalars are in reasonable agreement with the experiments and are consistent with earlier computations using flamlets and transported PDF methods for the stoichiometric flames, and transported PDF methods for the very lean flames. Sensitivity to chemical kinetics mechanism is also assessed.