  In this work, a novel Boussinesq system is put forward. The system is
naturally nonlinearly entropy/energy-stable, and is designed for problems with
sharply varying bathymetric features. The system is flexible and allows tuning
of the dispersive parameters to the relevant wavenumber range of the problem at
hand. We present a few such parameter sets, including one that tracks the
dispersive relation of the underlying Euler equations up to a nondimensional
wavenumber of about $30$.
  In the one-dimensional case, we design a stable finite-volume scheme and
demonstrate its robustness and accuracy in a suite of test problems including
Dingemans's wave experiment. We generalise the system to the two-dimensional
case and sketch how the numerical scheme can be straightforwardly generalised.
