  We prove uniqueness of static, asymptotically flat spacetimes with
non-degenerate black holes for three special cases of Einstein-Maxwell-dilaton
theory: For the coupling ``$\alpha = 1$'' (which is the low energy limit of
string theory) on the one hand, and for vanishing magnetic or vanishing
electric field (but arbitrary coupling) on the other hand. Our work generalizes
in a natural, but non-trivial way the uniqueness result obtained by
Masood-ul-Alam who requires both $\alpha = 1$ and absence of magnetic fields,
as well as relations between the mass and the charges. Moreover, we simplify
Masood-ul-Alam's proof as we do not require any non-trivial extensions of
Witten's positive mass theorem. We also obtain partial results on the
uniqueness problem for general harmonic maps.
