Lord Alderdice, the former Speaker of the Assembly and retired Irish civil servant Joe Brosnan.
BBC: NEWS | UK | Northern Ireland | Report backs Orde over IRA
The leader of the Alliance Party on the council, David Alderdice, said it had expected trust-building both inside and outside City Hall.
Fellow Liberal Democrat Lord Alderdice called on ministers to focus their "limited resources" on the Northern Ireland community "as a whole", instead of on individual cases.
But having achieved much of what his party wanted in a compromise deal, Lord Alderdice must now address fundamental questions about where the party goes from here.
Lord Alderdice has argued that such a deal contains all the necessary compromises to ensure the majority of people in Ireland, north and south, can support the deal.
He was succeeded by the current Lord Mayor David Alderdice, the brother of the former Alliance Party leader and current presiding officer of the Northern Ireland Assembly, Lord Alderdice.
BBC: News | UK Politics | Rival NI parties to share top jobs
However, only the British Government's nominees - Lord Alderdice and John Grieve - examine how devolved ministers and Northern Ireland parties are honouring their commitments under the Good Friday Agreement.
BBC: NEWS | UK | Northern Ireland | Report backs Orde over IRA
As leader of the non-sectarian Alliance Party, Lord Alderdice must deal with a challenge faced by all his predecessors - how to retain the support of voters from both sides of the community.
When the IRA called a ceasefire in 1994, Lord Alderdice showed a willingness to enter into discussions with Sinn Fein at a time when many in the unionist community still regarded that as unacceptable.
Liberal Democrat Lord Alderdice, who co-sponsored the amendment, said the issue was about making "absolutely clear" that concern for those with mental health issues "is every bit as great" as for people suffering from physical illnesses.
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