  We propose a new method to obtain the K -> pi pi amplitude from K -> pi which
allows one to fully account for the effects of final state interactions. The
method is based on a set of dispersion relations for the K -> pi pi amplitude
in which the weak Hamiltonian carries momentum. The soft pion theorem, which
relates this amplitude to the K -> pi amplitude, can be used to determine one
of the two subtraction constants - the second constant is at present known only
to leading order in chiral perturbation theory. We solve the dispersion
relations numerically and express the result in terms of the unknown higher
order corrections to this subtraction constant.
