GhostWhoVotes tweets Nielsen has the Coalition leading 54-46, down from 56-44 last month. The primary votes are 32% for Labor (up two), 45% for the Coalition (down two) and 11% for the Greens (down one). On both measures, this is Nielsen’s best result for Labor and its worst for the Coalition since the curious spike at the time of the February leadership challenge. Julia Gillard likewise has her first lead as preferred prime minister from Nielsen since February, being up three to 46% while Tony Abbott is down three to 45%. Both leaders are on 39% approval and 57% disapproval, which puts Gillard up two on approval and down one on disapproval, while Abbott is respectively steady and up one. Nielsen, for some reason, produces lower uncommitted results on this question than other pollsters.

GhostWhoVotes also offers full tables, which show the Coalition leading 55-45 in New South Wales (56-44 last month), at 50-50 in Victoria (51-49 in their favour last month), and leading 59-41 in Queensland (63-37), 53-47 in South Australia/Northern Territory (51-49) and 54-46 in Western Australia (65-35), remembering that small samples render the smaller state results especially of little meaning.

Also:

• Support for the carbon tax is steady since last month at 36%, and opposition steady at 59%. Only 3% of respondents (down two) believe the carbon tax and its attendant compensation have made them better off, 40% (up two) say they are worse off, and 54% (up two) say it has made no difference.

• Processing asylum seekers on Nauru and Manus Island is supported by 67% and opposed by 27%. Opinion on increasing the refugee intake is perfectly divided, with support at 48% and opposition at 49%.

UPDATE: Essential Research is not on board the swing-back-to-Labor train: primary votes are steady at 32% for Labor, 49% for the Coalition and 10% for the Greens, although rounding has nudged the two-party preferred back a point to Labor at 56-44.