Experimental evidence indicates that the stomatal conductance and nitrogen concentration ([N]) of foliage decline under CO2 enrichment, and that the percentage growth response to elevated CO2 is amplified under water limitation, but reduced under nitrogen limitation. We advance simple explanations for these responses based on an optimisation hypothesis applied to a simple model of the annual carbon-nitrogen-water economy of trees growing at a CO2-enrichment experiment at Oak Ridge, Tennessee, USA. The model is shown to have an optimum for leaf [N], stomatal conductance and leaf area index (LAI), where annual plant productivity is maximised. The optimisation is represented in terms of a trade-off between LAI and stomatal conductance, constrained by water supply, and between LAI and leaf [N], constrained by N supply. At elevated CO2 the optimum shifts to reduced stomatal conductance and leaf [N] and enhanced LAI. The model is applied to years with contrasting rainfall and N uptake. The predicted growth response to elevated CO2 is greatest in a dry, high-N year and is reduced in a wet, low-N year. The underlying physiological explanation for this contrast in the effects of water versus nitrogen limitation is that leaf photosynthesis is more sensitive to CO2 concentration ([CO2]) at lower stomatal conductance and is less sensitive to [CO2] at lower leaf [N].