Stomatal conductance, gs, responds both tothe immediate or local environment of the leaf, such as CO2 partialpressure and irradiance, and to root-sourced signals of water stress,particularly abscisic acid (ABA). Two models for the combined controlof gs were formulated and tested in sunflower(Helianthus annuus). First, several empirical models weretested for the local control, demonstrating that the Ball–Berrymodel [Ball, Woodrow & Berry (in Progress in PhotosynthesisResearch Vol. 4, pp. 5.221–5.224: M. Nijhoff,Dordrecht, The Netherlands) 1987] is consistently amongthe most accurate. A problem of statistical non-independence inthis model is shown to be minor. The model offers regularity ofparameter values among most species and, despite an oversimplicationin representing known humidity-response mechanisms, it incorporates othersignalling loops from CO2 and assimilation. In the firstcombined model, ABA as its concentration in xylem sap, [ABA]xy,down-regulates the slope, m, in the Ball–Berry modelby the factor gfac = exp(– β[ABA]xy).The ABA-induced reduction in gs decreases CO2 assimilation andsurface humidity, thus appearing to induce the local-control mechanismto amplify the ABA-induced stomatal closure. In the second combinedmodel, gs is estimated as the minimum of the local(Ball–Berry) response and the product gfac gs,max,with gs,max as a maximal unstressed conductance.Both models can predict gs from the external environmentalvariables with good accuracy (r2 near 0·8 over20-fold variations in gs). Further analyses showthat gs responds to humidity almost quadraticallyrather than linearly. It also responds to assimilation as a powerlaw with an exponent that is significantly less than 1. These limitations,shared by other models, suggest more research into biochemical signalling.