  We present a pedagogical case study how to combine micro-causality and
unitarity based on a perturbative approach. The method we advocate constructs
an analytic extrapolation of partial-wave scattering amplitudes that is
constrained by the unitarity condition. Suitably constructed conformal mappings
help to arrive at a systematic approximation of the scattering amplitude. The
technique is illustrated at hand of a Yukawa interaction. The typical case of a
superposition of strong short-range and weak long-range forces is investigated.
