Voucher entered separate from PO, how to manage PO encumbrance

We have some vouchers that were processed separately to pay on some invoices, but those vouchers were not linked to the POs they were paying against. Now we have effectively paid against the PO, but the encumbrance has not been relieved since it wasn't actually applied against the PO. What do you think is the appropriate way to resolve this issue? We can't void/reissue the payments, so my thought was we should either edit the PO to reduce it by what was paid, or to add new lines to the PO to reduce the encumbrance by what was paid. Your thoughts?