Eikonalized mini-jet cross-sections in $\gamma \gamma$ collisions

In this note we assess the validity and uncertainties in the predictions of the eikonalised mini-jet model for $\sigma^{inel}_{\gamma \gamma}$. We are able to find a choice of parameters where the predictions are compatible with the current data. Even for this restricted range of parameters the predictions at the high c.m. energies, which can be reached at the TeV energy $e^+e^-$ colliders, differ by about $\pm 25\%$. LEP 2 data can help pinpoint these parameters and hence reduce the uncertainties in the predictions.