  We improve our description of pion-pion scattering data by imposing
additional requirements to our previous fits, in the form of once-subtracted
Roy-like equations, while extending our analysis up to 1100 MeV. We provide
simple and ready to use parametrizations of the amplitude. In addition, we
present a detailed description and derivation of these once-subtracted
dispersion relations that, in the 450 to 1100 MeV region, provide an additional
constraint which is much stronger than our previous requirements of Forward
Dispersion Relations and standard Roy equations. The ensuing constrained
amplitudes describe the existing data with rather small uncertainties in the
whole region from threshold up to 1100 MeV, while satisfying very stringent
dispersive constraints. For the S0 wave, this requires an improved matching of
the low and high energy parametrizations. Also for this wave we have considered
the latest low energy Kl4 decay results, including their isospin violation
correction, and we have removed some controversial data points. These changes
on the data translate into better determinations of threshold and subthreshold
parameters which remove almost all disagreement with previous Chiral
Perturbation Theory and Roy equation calculations below 800 MeV. Finally, our
results favor the dip structure of the S0 inelasticity around the controversial
1000 MeV region.
