  In a series of papers we have applied several sum rules and forward
dispersion relations, to pion-pion scattering. We have found that some widely
used data sets fail to satisfy these constraints, and we have provided an
amplitude that describes data consistently with the dispersive tests.
Furthermore, we noted that the input and precision claimed in a Roy equation
analysis by Colangelo, Gasser and Leutwyler, lead to several mismatches with
some sum rules. Subsequently, Caprini, Colangelo, Gasser and Leutwyler claimed
that our Regge parametrization was incorrect. We collect here the answers to
their various claims, and try to clarify the points of agreement and
disagreement, showing experimental evidence that substantiates our results, and
that, in addition, their representation fails to satisfy all three forward
dispersion relations up to sqrt{s}<=800 MeV by several standard deviations.
