  We revisit the recently proposed method for the determination of the pi-pi
scattering length combination a_{0}-a_{2}, based on the study of the pi0 pi0
spectrum in K+ -> pi+ pi0 pi0. In view of a precision measurement, we discuss
here the effects due to smaller absorptive contributions to the K+ -> pi+ pi0
pi0 and K+ -> pi+ pi+ pi- amplitudes. We outline a method of analysis that can
lead to a precision determination of a_{0}-a_{2} and is based on very general
properties of the S matrix. The discussion of final-state rescattering and cusp
effects is also extended to the two K_L -> 3pi coupled channels. Thanks to the
present work, the theoretical error on the a_{0}-a_{2} combination extracted
from the K+ -> pi+ pi0 pi0 spectrum is reduced to about 5%. A further reduction
requires the evaluation of the effects arising from radiative corrections.
