Orange leaders have had a “cordial” meeting with Dr Richard Haass in Belfast as part of the ongoing talks process, but ruled out any return to a previously rejected parades plan.
Led by Grand Master Edward Stevenson, the delegation afterwards described the meeting as an “extremely beneficial” exercise.
Further meetings involving both the Orange Order and other loyal orders have been arranged for the coming weeks.
The Orange delegation included Grand Secretary Drew Nelson; Deputy Grand Master Rev Alistair Smyth; Assistant Grand Master Raymond Spiers and the Institution’s Director of Services, Dr David Hume.
After meeting Dr Haass, Rev Smyth said the previous parading proposals – put forward by a Sinn Fein/DUP working group in 2010 – were “too complicated”.
Rev Smyth told the BBC the search for an alternative to the Parades Commission was essential. “It [the Parades Commission] absolutely must go,” he said.