  We present an ansatz which enables us to construct heterotic/M-theory dual
pairs in four dimensions. It is checked that this ansatz reproduces previous
results and that the massless spectra of the proposed dual pairs agree. The new
dual pairs consist of M-theory compactifications on Joyce manifolds of $G_2$
holonomy and Calabi-Yau compactifications of heterotic strings. These results
are further evidence that M-theory is consistent on orbifolds. Finally, we
interpret these results in terms of M-theory geometries which are K3 fibrations
and heterotic geometries which are conjectured to be $T^3$ fibrations. Even
though the new dual pairs are constructed as non-freely acting orbifolds of
existing dual pairs, the adiabatic argument is apparently not violated.
