  We provide arguments for the existence of novel hereinafter called
poly-instanton corrections to holomorphic couplings in four-dimensional N=1
supersymmetric string compactifications. After refining quantitatively the
D-brane instanton calculus for corrections to the gauge kinetic function, we
explicitly apply it to the Type I toroidal orbifold defined in arXiv:0710.3080
and compare the results to the proposed heterotic S-dual model. This leads us
to the intriguing conclusion that N=1 string vacua feature a power tower like
proliferation of instanton corrections.
