  A new description for highly nonlinear potential water waves is suggested,
where weak 3D effects are included as small corrections to exact 2D equations
written in conformal variables. Contrary to the traditional approach, a small
parameter in this theory is not the surface slope, but it is the ratio of a
typical wave length to a large transversal scale along the second horizontal
coordinate. A first-order correction for the Hamiltonian functional is
calculated, and the corresponding equations of motion are derived for steep
water waves over an arbitrary inhomogeneous quasi-1D bottom profile.
