  We address the construction of non-supersymmetric vacua in heterotic
compactifications with intrinsic torsion and background fluxes. In particular,
we implement the approach of domain-wall supersymmetry breaking (DWSB)
previously developed in the context of type II flux compactifications. This
approach is based on considering backgrounds where probe NS5-branes wrapping
internal three-cycles and showing up as four-dimensional domain-walls do not
develop a BPS bound, while all the other BPS bounds characterizing the N=1
supersymmetric compactifications are preserved at tree-level. Via a scalar
potential analysis we provide the conditions for these backgrounds to solve the
ten-dimensional equations of motion including order \alpha' corrections. We
also consider backgrounds where some of the NS5-domain-walls develop a BPS
bound, show their relation to no-scale SUSY-breaking vacua and construct
explicit examples via elliptic fibrations. Finally, we consider backgrounds
with a non-trivial gaugino condensate and discuss their relation to
supersymmetric and non-supersymmetric vacua in the present context.
