We propose two Hamiltonian models to describe two-dimensional deep water waves propagating on the surface of an ideal incompressible three-dimensional fluid. The idea is based on taking advantage of the Zakharov equation for one-dimensional waves which can be written in the form of the so-called compact equations. We generalize these equations to the case of two-dimensional waves. As a test of our models we perform numerical simulations of the dynamics of standing waves in a water channel with smooth vertical walls. The results obtained in the proposed models are comparable, indicating that the models are similar to the original Zakharov equation.