  Hamiltonian models for the first three moments of the drift-kinetic
distribution function, namely the density, the fluid velocity and the parallel
pressure, are derived from the Hamiltonian structure of the drift-kinetic
equations. The link with the water-bag closure is established, showing that,
unlike the one-dimensional Vlasov equations, these solutions are the only
Hamiltonian fluid reductions for the drift-kinetic equation. These models are
discussed through their equations of motion and their Casimir invariants.
