We formulate a new second-order closure turbulence model by employing a recent closure for the pressure– temperature correlation at the equation level. As a result, we obtain new heat flux equations that avoid the longstanding issue of a finite critical Richardson number. The new, structurally simpler model improves on the Mellor–Yamada and Galperin et al. models; a key feature includes enhanced mixing under stable conditions facilitating agreement with observational, experimental, and high-resolution numerical datasets. The model predicts a planetary boundary layer height deeper than predicted by models with low critical Richardson numbers, as demonstrated in single-column model runs of the GISS ModelE general circulation model.