Abstract The joint-scalar transported PDF approach is applied to compute freely propagating turbulent premixed flames with burning velocities determined for a range of turbulence intensities and fuel mixtures. The computed cases include rich hydrogen, stoichiometric and lean methane and stoichiometric ethane flames. The aim of the study is to investigate the sensitivity of predictions to different closure elements and to explore the predictive capabilities of the method. The work features extended chemistry closures with a systematically reduced mechanism featuring 142 reactions, 15 solved and 14 steady-state species applied for methane and ethane flames. A detailed sub-mechanism featuring 21 reactions and 9 solved species was used for the hydrogen flames. It is shown that the scaling of turbulent burning velocities with respect to turbulence intensity variations can be significantly improved through the application of an extended multi-scale scalar dissipation rate closure. Furthermore, the impact of molecular transport in physical space is explored through the derivation and inclusion of an explicit correction term applicable at the leading flame edge. It is shown that the impact is modest for fuels such as hydrogen and ethane, but that it can be expected to be significant for fuels with large Zeldovich numbers.