  We derived consistently, according to the second order perturbation approach,
the extended KdV equation for an uneven bottom for the case of
$\alpha=O(\beta)$ and $\delta=O(\beta^2)$. This equation can be obtained only
when the bottom is given by a piecewise linear function. For the case of
$\alpha=O(\beta)$ and $\delta=O(\beta)$, a unidirectional wave equation is
derived in the first order approach with the same limitation for the bottom
profile.
