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 new dual pairs agree. The new dual pairs consist of M-theory compactifications on Joyce manifolds of G2 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 T3 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.