  We consider higher derivative corrections of the type D^{2k} R^2 in the
effective action of the D3-brane with trivial normal bundle. Based on the
perturbative disc and annulus amplitudes, and constraints of supersymmetry and
duality, we argue that these interactions are protected, at least for small
values of k. Their coefficient functions receive only a finite number of
perturbative contributions, and non-perturbative contributions from
D-instantons. We propose expressions for these modular forms for low values of
k.
