  We check quantitatively the validity of some popular phenomenological
approaches of QCD in simple models. Dispersion sum rules are considered within
the ladder approximation of a field-theoretic model with OPE given by ordinary
loop diagrams which are computable for any number of loops. A correlator of two
currents within the model complies with all requirements of standard QCD sum
rules approach for fitting low-lying resonances such as fast convergence and
good stability while the exact spectrum contains no resonance. Optimized PT as
it is inspired by the principle of minimal sensitivity is analyzed within a
quantum mechanical model and is shown to work well as compared to pure
asymptotic expansion in the coupling constant or Pad\'e approximation.
Renormalon technique is tested within another quantum mechanical model and is
found to fail to detect its low-energy structure.
