  The classical bond-fluctuation model (BFM) is an efficient lattice Monte
Carlo algorithm for coarse-grained polymer chains where each monomer occupies
exclusively a certain number of lattice sites. In this paper we propose a
generalization of the BFM where we relax this constraint and allow the overlap
of monomers subject to a finite energy penalty $\overlap$. This is done to vary
systematically the dimensionless compressibility $g$ of the solution in order
to investigate the influence of density fluctuations in dense polymer melts on
various s tatic properties at constant overall monomer density. The
compressibility is obtained directly from the low-wavevector limit of the
static structure fa ctor. We consider, e.g., the intrachain bond-bond
correlation function, $P(s)$, of two bonds separated by $s$ monomers along the
chain. It is shown that the excluded volume interactions are never fully
screened for very long chains. If distances smaller than the thermal blob size
are probed ($s \ll g$) the chains are swollen acc ording to the classical
Fixman expansion where, e.g., $P(s) \sim g^{-1}s^{-1/2}$. More importantly, the
polymers behave on larger distances ($s \gg g$) like swollen chains of
incompressible blobs with $P(s) \si m g^0s^{-3/2}$.
