We study heterotic E8 × E8 models that are dual to compactifications of F-theory and type IIA string on certain classes of elliptically fibered Calabi-Yau manifolds. Different choices for the specific torus in the fibration have heterotic duals that are most easily understood in terms of E8 × E8 models with gauge backgrounds of type H × U(1)8-d, where H is a non-Abelian factor. The case with d = 8 corresponds to the well known E8 × E8 compactifications with non-Abelian instanton backgrounds (k1, k2) whose F-theory duals are built through compactifications on fibrations of the torus P(1,2,3)2 over Fn. The new cases with d < 8 correspond to other choices for the elliptic fiber over the same base and yield unbroken U(1)'s, some of which are anomalous and acquire a mass by swallowing zero modes of the antisymmetric BMN field. We also study transitions to models with no tensor multiplets in D = 6 and find evidence of Ed instanton dynamics.