  We investigate a model QCD sum rule for the pion wave function
$\varphi_{\pi}(x)$ based on the non-diagonal correlator whose perturbative
spectral density vanishes and $\Phi(x,M^2)$, the theoretical side of the sum
rule, consists of condensate contributions only. We study the dependence of
$\Phi(x,M^2)$ on the Borel parameter $M^2$ and observe that $\Phi(x,M^2)$ has a
humpy form, with the humps becoming more and more pronounced when $M^2$
increases. We demonstrate that this phenomenon reflects just the oscillatory
nature of the higher states wave functions, while the lowest state wave
function $\varphi_{\pi}(x)$ extracted from our QCD sum rule analysis,has no
humps, is rather narrow and its shape is close to the asymptotic form
$\varphi_{\pi}^{as}(x) = 6x(1-x)$.
