  We show that the minimal Gaussian model of nonlocal vacuum quark and
quark-gluon condensates in QCD generates the non-transversity of vector current
correlators. We suggest the improved Gaussian model of the nonperturbative QCD
vacuum, which respects QCD equations of motion and minimizes the revealed
gauge-invariance breakdown. We obtain the refined values of pion distribution
amplitude (DA) conformal moments using the improved QCD vacuum model and
construct the allowed region for Gegenbauer coefficients a_2 and a_4 of the
pion DA.
