  We use our former results on pi+pi- S-wave obtained in a nearly
assumption-free way from the 17.2 GeV/c data to predict the pi0pi0 S--wave. The
predictions are compared with the recent results of the E852 experiment at 18.3
GeV/c. A good agreement is found for only one (the "down-flat") solution while
the second one (the "up-flat") is excluded by the pi0pi0 data. Thus the
long-standing "up-down" ambiguity has been finally resolved in favour of the
S-wave intensity which stays large and nearly constant up to the KK-bar
threshold. A joint analysis of both sets of data leads to a reduction of errors
for this solution.
