$F^{4}$ Terms in N=4 String Vacua

We discuss $F_{\mu\nu}^4$ terms in toroidal compactifications of type-I and heterotic SO(32) string theory. We give a simple argument why only short BPS multiplets contribute to these terms at one loop, and verify heterotic-type-I duality to this order. Assuming exact duality, we exhibit in the heterotic calculation non-zero terms that are two-loop, three-loop and non-perturbative on the type-I side.