  We consider a mixture of single-component bosonic and fermionic atoms in an
array of coupled one-dimensional "tubes". For an attractive Bose-Fermi
interaction, we show that the system exhibits phase separation instead of the
usual collapse. Moreover, above a critical inter-tube hopping, all first-order
instabilities disappear in both attractive and repulsive mixtures. The
possibility of suppressing instabilities in this system suggests a route
towards the realization of paired phases, including a superfluid of p-wave
pairs unique to the coupled-tube system, and quantum critical phenomena.
