Current estimates of gross primary productivity (GPP) of the terrestrial biosphere vary widely, from 100 to 175 Gt C year-1. Ecosystem GPP cannot be measured directly, and is commonly estimated using models. Among the many parameters in those models, three leaf parameters have strong influences on the modelled GPP: leaf mass per area, leaf lifespan and leaf nitrogen concentration. The first two parameters affect the modelled canopy leaf area and the last two determine the maximal leaf photosynthetic rate. Ecological studies have firmly established that these three parameters are significantly correlated at regional to global scales, but this knowledge is yet to be used in predicting global GPP. We hypothesize that incorporating multi-trait covariance can reduce uncertainties of model predictions in a way likely to provide improved realism. Using the Australian community land surface model (CABLE), we find that correlations among these three parameters reduce the variance among GPP estimates by CABLE by over 20% for shrub, C4 grassland and tundra, and by between 5% and 20% for most other PFTs, as compared with the simulated GPP without considering the correlations. Globally the correlations do not alter the mean but reduce the variance of modeled GPP by CABLE by 28% and result in fewer extremely high or extremely low (and unlikely) global GPP predictions. Therefore correlations among the three leaf parameters, and possibly other parameters, can be used as a significant constraint on the estimates of model parameters or predictions by those models.