The exact string coupling dependence of higher derivative terms in the type IIA and type IIB effective action is highly constrained by a combination of duality symmetries and by results from perturbative string theory. For example, we show that terms of the form D to the 2k times R to the 4th in type IIA theory should receive no perturbative contributions beyond genus k (k greater than 0). We also propose that the exact modular functions of general type IIB higher derivative terms are determined by a Poisson equation on the fundamental domain of the moduli space.