  After discussing some general problems for heterotic compactifications
involving fivebranes we construct bundles, built as extensions, over an
elliptically fibered Calabi-Yau threefold. For these we show that it is
possible to satisfy the anomaly cancellation topologically without any
fivebranes. The search for a specific Standard model or GUT gauge group
motivates the choice of an Enriques surface or certain other surfaces as base
manifold. The burden of this construction is to show the stability of these
bundles. Here we give an outline of the construction and its physical
relevance. The mathematical details, in particular the proof that the bundles
are stable in a specific region of the K\"ahler cone, are given in the
mathematical companion paper math.AG/0611762.
