  The main purpose of scattering experiments is to unveil the underlying
structure of the colliding particles and their interaction. Typically one
measures scattering observables (cross sections and polarizations) at discrete
angles and energies and mutually consistent data may validate or falsify
proposed theories or models. However, the accumulation of data from different
laboratories while potentially improves the statistical significance it may
sometimes generate mutually inconsistent data as a side-effect. Thus, some
decision has to be made on what are the maximal amount of data which are
mutually compatible. We show elastic $\pi N $ and $NN$ scattering as prominent
examples where this selection is called for. We discuss how it can be done in a
self-consistent manner invoking a principle of maximal consensus of the
database and with the help of a sufficiently flexible model involving a minimal
number of theoretical assumptions. In the NN case this has become possible with
a combination of long distance field theoretical constraints at the hadronic
level such as pion exchanges and electromagnetic effects and a coarse graining
of the unknown interaction over the shortest de Broglie wavelength being probed
in the scattering process.
