Former New Zealand Prime Minister Helen Clark will be hoping for a stronger finish in the second secret ballot taking place at the United Nations on who should become the next Secretary-General.
The UN Security Council is due to hold the second of a number of planned informal or "straw" polls on the candidates in New York.
Although the vote is taken behind closed doors, the results are expected to be leaked and should be known on Saturday morning (NZT).
Twelve candidates - six men and six women - are vying to be the one to hold the world's top diplomatic post and replace current Secretary-General Ban Ki-moon.
The 15-member Security Council will have a ballot for each candidate, with members deciding whether to 'encourage', 'discourage' or have 'no opinion'.
Disappointing first round
Going into the first straw poll, Miss Clark, who is the current Administrator of the UN Development Programme, was considered one of the favourites - mainly because she is a woman with government, executive and UN experience.
But in the first straw poll held last month, she came a surprising sixth, in the middle of the pack.
She won eight 'encourage' votes, five 'discourage' and two of 'no opinion'. The key for her in this round is to get rid of the 'discourage' votes.
The way Mr Ban won 10 years ago was by consistently being the candidate with no discourage votes and therefore acceptable to everyone.
Foreign Minister Murray McCully said officials in Miss Clark's campaign team would have been trying to talk to those who might have placed 'discourage' votes and it was still very early in the process.
Former Portuguese Prime Minister and UN Refugee Agency head Antonio Guterres won the first poll with 12 encourage votes and three no opinions.
He edged out former Slovenian President Danilo Turk, who got 11 encourages, two discourages and two no opinions.
Diplomats believe if Mr Gutteres has another good round, he could well cement his place as the next Secretary-General.
Push for a woman
There has been a big push this year to try and lobby for the UN to make history and appoint a woman leader, with nearly a third of the 193 UN member states expressing support for such a move.
Colombian UN Ambassador Maria Emma Mejia said the Group of Friends for a Woman Secretary-General had succeeded in putting gender equality on the UN agenda and attracting six female candidates, but there was disappointment that none had made it to the top in the first poll.
"I wouldn't close the possibility for a woman and I would still stress to Security Council members to consider a woman," she said.
"The issue of gender has captured people's attention."
The Security Council will continue to hold secret ballots until a consensus is reached on a candidate.
Diplomats said the aim was for the council to recommend a candidate to the 193-member General Assembly for election in September or October.
In reality, it's the five permanent veto-wielding council members - the United States, Russia, Britain, China and France - who must agree on a candidate and put them forward to the General Assembly.
The UN Secretary-General oversees some 41,000 civilian staff and 16 peacekeeping operations with more than 101,000 troops and police.
The core annual UN budget is $US2.7 billion, while the peacekeeping budget is nearly $US8bn.