We analyse the buy-back of its debt by an LDC. Contrary to the analyses that were previously done on this subject, we assume that the debtor can hide its transactions behind the veil of a fictitious operator: the banks, we assume, cannot discriminate intra-bank transactions from buy-backs by the debtor itself. With this assumption, the lenders set the price by (rationally) taking account of the country's incentive to repurchase its debt. Will the debtor undertake a buy-back of its debt? The answer is a qualified yes. Large buy-backs will take place. With a continuum of debtors (whose cash constraints are not perfectly known to the banks), the rich debtors will attempt to repurchase as much of their debt as their cash constraint allows them to. This is shown to be Pareto-improving for both the banks and the debtor country.