  We prove the existence of the weak solutions to the compressible
Navier--Stokes system with barotropic pressure $p(\varrho)=\varrho^\gamma$ for
$\gamma\geq 9/5$ in three space dimension. The novelty of the paper is the
approximation scheme that instead of the classical regularization of the
continuity equation (based on the viscosity approximation $\ep \Delta \varrho$)
uses more direct truncation and regularisation of nonlinear terms an the
pressure. This scheme is compatible with the Bresch-Jabin compactness criterion
for the density. We revisit this criterion and prove, in full rigour, that it
can be applied in our approximation at any level.
