  We study heterotic/type I duality in d=8,9 uncompactified dimensions. We
consider the special (``BPS saturated'') F^4 and R^4 terms in the effective
one-loop heterotic action, which are expected to be non-perturbatively exact.
Under the standard duality map these translate to tree-level, perturbative and
non-perturbative contributions on the type I side. We check agreement with the
one-loop open string calculation, and discuss the higher-order perturbative
contributions, which arise because of the mild non-holomorphicities of the
heterotic elliptic genus. We put the heterotic world-sheet instanton
corrections in a form that can be motivated as arising from a D-brane instanton
calculation on the type-I side.
