What pi - pi scattering tells us about chiral perturbation theory

We describe a rearrangement of the standard expansion of the symmetry-breaking part of the QCD effective Lagrangian that includes into each order additional terms which in the standard chiral perturbation theory ([chi]PT) are relegated to higher orders. The new expansion represents a systematic and unambiguous generalization of the standard [chi]PT, and is more likely to converge rapidly. It provides a consistent framework for a measurement of the importance of additional higher-order'' terms whose smallness is usually assumed but has never been checked. A method of measuring, among other quantities, the QCD parameters [ital [cflx m]][l angle][ital [bar q]q][r angle] and the quark mass ratio [ital m][sub [ital s]]/[ital [cflx m]] is elaborated in detail. The method is illustrated using various sets of available data. Both of these parameters might be considerably smaller than their respective leading-order standard [chi]PT values. The importance of new, more accurate, experimental information on low-energy [pi]-[pi] scattering is stressed.