  The correlation function measured in ultrarelativistic nuclear collisions is
strongly non-Gaussian. Using two different models we study which effects can
influence its shape and how much. In particular, we focus on the
parametrizations expressed with the help of L\'evy-stable distributions. We
show that the L\'evy index may deviate substantially from 2 due to non-critical
effects such as resonance decays, event-by-event fluctuations and functional
dependence on $Q_{LI}$ or similar. We also study the corrections including the
first-order L\'evy expansion.
