F4 terms in N = 4 string vacua

We discuss F μν 4 terms in torroidal 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.