We present two new model equations for the unidirectional propagation
of long waves in dispersive media for the specific purpose of modeling
water waves. The derivation of the new equations uses a Pade(2,2)
approximation of the phase velocity that arises in the linear water
wave theory. Unlike the Korteweg-deVries (KdV) equation and similarly
to the Benjamin-Bona-Mahony (BBM) equation, our models have a bounded
dispersion relation. At the same time, the equations we propose provide
the best approximation of the phase velocity for small wave numbers that
can be obtained with third-order equations. We note that the new model
equations can be transformed into previously studied models, such as the
BBM and the Burgers-Poisson equations. It is therefore straightforward
to establish the existence and uniqueness of solutions to the new
equations. We also show that the distance between the solutions of one
of the new equations, the KdV equation, and the BBM equation, is of the
small order that is formally neglected by all models.