Support among Labour MPs for the party leadership has Grant Robertson just ahead of David Parker with 11 and 9 supporters respectively, and both are some way ahead of Nanaia Mahuta and Andrew Little with six supporters each, soundings by the New Zealand Herald suggest.
Many expect the contest to come down to Mr Little and Mr Robertson, but Mr Parker appears to have more caucus support than Mr Little.
Mr Little, however, is expected to attract the majority of the affiliated unions' votes, and Ms Mahuta seems likely to be the first one eliminated in the preferential voting system.
That means second and possibly third preferences will be crucial.
Candidates are said to be lobbying as strongly for second preferences as for first.