Instantaneous, three-dimensional scalar dissipation rates of the reaction progress variable are measured in turbulent premixed Bunsen flames of lean hydrocarbon/air mixtures with the two-sheet, two-dimensional Rayleigh scattering technique. The flames investigated are located in the turbulent flame-front regime on a newly proposed combustion diagram for premixed flames. The conditionally-averaged mean scalar dissipation rates, $N_{zeta}$ are found to be lower than the calculated laminar values, indicating a locally broadened flame front. In agreement with previous measurements, the maximum of $N_{zeta}$, decreases strongly with increasing Karlovitz numbers. The conditional probability density functions are close to a log-normal distribution for scalar dissipation rates conditioned at the progress variable value where the scalar dissipation is maximum in unstretched laminar flame calculations. The time scale for the Favre-averaged mean scalar dissipation rate decreases in general across the turbulent flame brush from the unburnt to burnt side.