  We present a calculation of nuclear matter which goes beyond the usual
quasi-particle approximation in that it includes part of the off-shell
dependence of the self-energy in the self-consistent solution of the
single-particle spectrum. The spectral function is separated in contributions
for energies above and below the chemical potential. For holes we approximate
the spectral function for energies below the chemical potential by a
$\delta$-function at the quasi-particle peak and retain the standard form for
energies above the chemical potential. For particles a similar procedure is
followed. The approximated spectral function is consistently used at all levels
of the calculation. Results for a model calculation are presented, the main
conclusion is that although several observables are affected by the inclusion
of the continuum contributions the physical consistency of the model does not
improve with the improved self-consistency of the solution method. This in
contrast to expectations based on the crucial role of self-consistency in the
proofs of conservation laws.
