  The metric on the hypermultiplet moduli space of Calabi-Yau compactifications
of type II string theory is known to receive D-brane and NS5-brane instanton
corrections. We compute explicit expressions for these corrections in the
one-instanton approximation, but to all orders in the string coupling expansion
around the instantons. As a consistency check, we prove that in the case of one
(universal) hypermultiplet, the resulting metric fits the Przanowski
description of self-dual Einstein spaces. We also show that in the small string
coupling limit the metric acquires a certain square structure, consistently
with expectations from the string amplitudes analysis. This result provides
explicit predictions for yet mysterious string amplitudes in the presence of
NS5-branes.
