  We propose a scenario to stabilize all geometric moduli - that is, the
complex structure, Kahler moduli and the dilaton - in smooth heterotic
Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is
accomplished using the gauge bundle required in any heterotic compactification,
whose perturbative effects on the moduli are combined with non-perturbative
corrections. We argue that, for appropriate gauge bundles, all complex
structure and a large number of other moduli can be perturbatively stabilized -
in the most restrictive case, leaving only one combination of Kahler moduli and
the dilaton as a flat direction. At this stage, the remaining moduli space
consists of Minkowski vacua. That is, the perturbative superpotential vanishes
in the vacuum without the necessity to fine-tune flux. Finally, we incorporate
non-perturbative effects such as gaugino condensation and/or instantons. These
are strongly constrained by the anomalous U(1) symmetries which arise from the
required bundle constructions. We present a specific example, with a consistent
choice of non-perturbative effects, where all remaining flat directions are
stabilized in an AdS vacuum.
