  We investigate to what extent a suitably chosen system Hamiltonian can
counteract local dissipative processes and preserve entanglement in the
stationary state. The results determine prospects and limitations of
dissipative state preparation schemes based on natural dissipative processes --
in contrast to engineered, typically non-local dissipative schemes. As an
exemplary case, we determine the stationary state of two spontaneously decaying
two-level systems with optimal entanglement properties. The corresponding
system Hamiltonian is derived, and its possible experimental implementation is
discussed in detail. Finally, we discuss generalizations for many qubits.
