  We discuss finite-volume computations of two-body hadronic decays below the
inelastic threshold (e.g. $K\to\pi\pi$ decays). The relation between
finite-volume matrix elements and physical amplitudes, recently derived by
Lellouch and L\"uscher, is extended to all elastic states under the inelastic
threshold. We present a detailed comparison of our approach with that of
Lellouch and L\"uscher and discuss the possible limitations of the method which
could arise due to the presence of inelastic thresholds. We also examine a
standard alternative method which can be used to extract the real part of the
decay amplitude from correlators of the form $< 0 |T[\pi\pi{\cal H}_WK ]| 0 >$.
We show that in this case there are finite-volume corrections which vanish as
inverse powers of the volume, which cannot be removed by a multiplicative
factor.
