  We construct new smooth solutions to the Hull-Strominger system, showing that
the Fu-Yau solution on torus bundles over K3 surfaces can be generalized to
torus bundles over K3 orbifolds. In particular, we prove that, for $13 \leq k
\leq 22$ and $14\leq r\leq 22$, the smooth manifolds $S^1\times
\sharp_k(S^2\times S^3)$ and $\sharp_r (S^2 \times S^4) \sharp_{r+1} (S^3
\times S^3)$, have a complex structure with trivial canonical bundle and admit
a solution to the Hull-Strominger system.
