  The RBC and UKQCD collaborations have recently proposed a procedure for
computing the K_L-K_S mass difference. A necessary ingredient of this procedure
is the calculation of the (non-exponential) finite-volume corrections relating
the results obtained on a finite lattice to the physical values. This requires
a significant extension of the techniques which were used to obtain the
Lellouch-Luscher factor, which contains the finite-volume corrections in the
evaluation of non-leptonic kaon decay amplitudes. We review the status of our
study of this issue and, although a complete proof is still being developed,
suggest the form of these corrections for general volumes and a strategy for
taking the infinite-volume limit. The general result reduces to the known
corrections in the special case when the volume is tuned so that there is a
two-pion state degenerate with the kaon.
