  We study a brane-world cosmological scenario with local inhomogeneities
represented by black holes. The brane is asymmetrically embedded into the bulk.
The black strings/cigars penetrating the Friedmann brane generate a
Swiss-cheese type structure. This universe forever expands and decelerates, as
its general relativistic analogue. The evolution of the cosmological fluid
however can proceed along four branches, two allowed to have positive energy
density, one of them having the symmetric embedding limit. On this branch a
future pressure singularity can arise for either (a) a difference in the
cosmological constants of the cosmological and black hole brane regions (b) a
difference in the left and right bulk cosmological constants. While the
behaviour (a) can be avoided by a redefinition of the fluid variables, (b)
establishes a critical value of the asymmetry over which the pressure
singularity occurs. We introduce the pressure singularity censorship which
bounds the degree of asymmetry in the bulk cosmological constant. We also show
as a model independent generic feature that the asymmetry source term due to
the bulk cosmological constant increases in the early universe. In order to
obey the nucleosynthesis constraints, the brane tension should be constrained
therefore both from below and from above. With the maximal degree of asymmetry
obeying the pressure singularity censorship, the higher limit is 10 times the
lower limit. The degree of asymmetry allowed by present cosmological
observations is however much less, pushing the upper limit to infinity.
