  We examine the duality between type 0 noncritical strings and topological
B-model strings, with special emphasis on the flux dependence. The former
theory is known to exhibit holomorphic factorisation upto a subtle
flux-dependent disc term. We give a precise definition of the B-model dual and
propose that it includes both compact and noncompact B-branes. The former give
the factorised part of the free energy, while the latter violate holomorphic
factorisation and contribute the desired disc term. These observations are
generalised to rational radii, for which we derive a nonperturbatively exact
result. We also show that our picture extends to a proposed alternative
topological-anti-topological picture of the correspondence for type 0 strings.
