  We explore a new type of discretizations of lattice dynamical models of the
Klein-Gordon type relevant to the existence and long-term mobility of nonlinear
waves. The discretization is based on non-holonomic constraints and is shown to
retrieve the "proper" continuum limit of the model. Such discretizations are
useful in exactly preserving a discrete analogue of the momentum. It is also
shown that for generic initial data, the momentum and energy conservation laws
cannot be achieved concurrently. Finally, direct numerical simulations
illustrate that our models yield considerably higher mobility of strongly
nonlinear solutions than the well-known "standard" discretizations, even in the
case of highly discrete systems when the coupling between the adjacent nodes is
weak. Thus, our approach is better suited for cases where an accurate
description of mobility for nonlinear traveling waves is important.
