  We introduce a method of using the a dual type IIA string to compute
alpha'-corrections to the moduli space of heterotic string compactifications.
In particular we study the hypermultiplet moduli space of a heterotic string on
a K3 surface. One application of this machinery shows that type IIB strings
compactified on a Calabi-Yau space suffer from worldsheet instantons, spacetime
instantons and, in addition, "mixed" instantons which in a sense are both
worldsheet and spacetime. As another application we look at the hyperkaehler
limit of the moduli space in which the K3 surface becomes an ALE space. This is
a variant of the "geometric engineering" method used for vector multiplet
moduli space and should be applicable to a wide range of examples. In
particular we reproduce Sen and Witten's result for the heterotic string on an
A1 singularity and a trivial bundle and generalize this to a collection of E8
point-like instantons on an ALE space.
