  Adding quenched disorder to the one-dimensional asymmetric exclusion process
is known to always induce phase separation. To test the robustness of this
result, we introduce two modifications of the process that allow particles to
bypass defect sites. In the first case, particles are allowed to jump l sites
ahead with the probability p_l ~ l^-(1+sigma), where sigma>1. By using Monte
Carlo simulations and the mean-field approach, we show that phase coexistence
may be absent up to enormously large system sizes, e.g. lnL~50, but is present
in the thermodynamic limit, as in the short-range case. In the second case, we
consider the exclusion process on a quadratic lattice with symmetric and
totally asymmetric hopping perpendicular to and along the direction of driving,
respectively. We show that in an anisotropic limit of this model a regime may
be found where phase coexistence is absent.
