BAA, the British airports operator that runs London’s Heathrow Airport, has managed to win the support of hedge fund Polygon Investment Managers for a new funding structure.

Polygon, which owns slightly more than 25% of BAA’s 2031-dated bonds, had been withholding its votes in favor of the plan in an effort to win further concessions. BAA, which also operates London’s Gatwick and Stansted airports, as well as four airports in Scotland, needed at least 75% approval from bondholders in each series of bonds.

BAA said today that it had won “overwhelming” support from holders of all nine series of bonds. It is unclear what, if any, additional concessions were made to win over Polygon.

Under the plan, BAA will “migrate” the £4.7 billion in bonds to new investment-grade debt backed by the three London Airports and its shuttle train to downtown London, Heathrow Express.