  We present examples where expressions for $\exp(\hat{A}+\hat{B})$ can be
derived even though the operators (or superoperators) $\hat{A}$ and $\hat{B}$
do not commute in a manner that leads to known factorizations. We apply our
factorization to the case of a Lindblad operator modeling single photon decay
and to a binary Glauber-Fock photonic lattice.
