  We consider Schr\"odinger operators on [0,\infty) with compactly supported,
possibly complex-valued potentials in L^1([0,\infty)). It is known (at least in
the case of a real-valued potential) that the location of eigenvalues and
resonances determines the potential uniquely. From the physical point of view
one expects that large resonances are increasingly insignificant for the
reconstruction of the potential from the data. In this paper we prove the
validity of this statement, i.e., we show conditional stability for finite
data. As a by-product we also obtain a uniqueness result for the inverse
resonance problem for complex-valued potentials.
