  Global fits to the shape of the first QCD Laplace sum rule exhibiting
sensitivity to pion-resonance [$\Pi (1300)$] parameters are performed, leading
to predictions for the pion-resonance mass and decay constant. Two scenarios
are considered which differ only in their treatment of the dimension-six quark
condensate $< O_6>$. The first scenario assumes an effective scale for $< O_6>$
from other sum-rule applications which is assumed to be independent of the
physical value of the quark mass, while the second scenario requires
self-consistency between the value of $< O_6>$ and the current algebra
constraint $2m< \bar q q>=-f_\pi^2m_\pi^2$. Predictions of the pion-resonance
mass $M_\pi$ and decay constant $F_\pi$ are obtained in these two scenarios. A
byproduct of this analysis is a prediction of the renormalization-group
invariant quark mass $(\hat m_u+\hat m_d)/2$.
