  The systematic errors inherent in the QCD sum rule approach to meson
wavefunctions are examined in the context of QCD in 1+1 spacetime dimensions in
the large N limit where the theory is exactly solvable. It is shown that the
truncation of high momentum modes induced in a lattice discretization
automatically produces a Chernyak-Zhitnitsky \cite{CZ} type meson wavefunction.
Such a truncation alters the balance of leading and higher twist terms in
correlators. We find that the reliable extraction of (a few) higher moments is
possible provided a reasonably accurate uniform approximation to the Euclidean
correlator over a suitable $Q^2$ range is available, but that the extracted
values are particularly sensitive to the balance of lower and higher twist
contributions. Underestimates of lower twist contributions or overestimates of
the highest twist term may lead to too high values for the second and fourth
moments of the pion wavefunction, suggesting a doubly peaked structure of the
Chernyak-Zhitnitsky type.
