New reacting flow models are proposed and tested for all pressure fluctuation covariances that are known to play a crucial role in the second moment closure of the averaged equations of turbulent flows. The models, which are applicable to the thin laminar flamelet regime of premixed turbulent combustion, are based on a partitioning of each covariance into contributions from reactants, products, and thin flamelets. Intermittency between the conditional mean pressure gradients in reactants and products is found to play an important role in the resulting expressions. The proposed models are extensively tested using two-dimensional direct numerical simulation (DNS) of premixed combustion in decaying turbulence. The compressible flow code includes effects of finite heat release controlled by an assumed global reaction rate mechanism. Good agreement is found between the model expressions and pressure fluctuation covariances evaluated from DNS.