  It is well known that a spherically symmetric compact star whose energy
density decreases monotonically possesses an upper bound on its mass-to-radius
ratio, $2M/R\leq 8/9$. However, field configurations typically will not be
compact. Here we investigate non-compact static configurations whose matter
fields have a slow global spatial decay, bounded by a power law behavior. These
matter distributions have no sharp boundaries. We derive an upper bound on the
fundamental ratio max_r{2m(r)/r} which is valid throughout the bulk. In its
simplest form, the bound implies that in any region of spacetime in which the
radial pressure increases, or alternatively decreases not faster than some
power law $r^{-(c+4)}$, one has $2m(r)/r \leq (2+2c)/(3+2c)$. [For $c \leq 0$
the bound degenerates to $2m(r)/r \leq 2/3$.] In its general version, the bound
is expressed in terms of two physical parameters: the spatial decaying rate of
the matter fields, and the highest occurring ratio of the trace of the pressure
tensor to the local energy density.
