A recent analysis (Lipatnikov et al., 2020) of complex-chemistry direct numerical simulation (DNS) data obtained from lean hydrogen-air flames associated with corrugated-flame (case A), thin-reaction-zone (case B), and broken-reaction-zone (case C) regimes of turbulent burning has shown that the flamelet concept (i) can predict mean concentrations of various species in those flames if the probability density function (PDF) for the fuel-based combustion progress variable c is extracted from the DNS data, but (ii) poorly performs for the mean rate W¯c of product creation. These results suggest applying the concept to evaluation of mean species concentration (but not the mean rate) in combination with another closure relation for W¯c whose predictive capabilities are better. This proposal is developed in the present paper whose focus is placed on studying a new flamelet-based presumed PDF P(c) for predictions of mean concentration of radicals in engineering computational fluid dynamics (CFD) applications. Analysis of the DNS data shows that (i) the flamelet PDF performs well at intermediate values of c in cases A and B, but should be truncated at small and large c, (ii) modeling P(c) in the radical recombination zone (i.e., at large c) is of importance for predicting mean concentrations of H,O, and OH. Accordingly, the flamelet PDF is truncated and combined with a uniform P(c) at large c. Moreover, the mean rate W¯c extracted from the DNS data is used to calibrate the PDF (the rate is considered to be given by another model). Assessment of the approach against the DNS data shows that it well predicts mean density, temperature, and concentrations of reactants, product, and the aforementioned radicals in cases A and B. In case C, the approach performs worse for OandOH at large c¯ and moderately underestimates the mean concentration of H in the entire flame brush.