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 $varphi_{pi}^{as}(x) = 6x(1-x)$.
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