  We determine the one-instanton corrections to the universal hypermultiplet
moduli space coming both from Euclidean membranes and NS-fivebranes wrapping
the cycles of a (rigid) Calabi-Yau threefold. These corrections are completely
encoded by a single function characterizing a generic four-dimensional
quaternion-Kahler metric without isometries. We give explicit solutions for
this function describing all one-instanton corrections, including the
fluctuations around the instanton to all orders in the string coupling
constant. In the semi-classical limit these results are in perfect agreement
with previous supergravity calculations.
