The Senate has been kinder to Malcolm Turnbull than Tony Abbott.
A new study by Hawker Britton shows Labor, the Greens and key crossbenchers have been more likely to vote for motions brought by the Turnbull government than Mr Abbott's regime.
The study comes as the government seeks to change Senate voting rules which are likely to demolish micro-parties and make it easier for candidates from the bigger parties to get elected.
Overall, there has been a nine per cent rise in support for government "divisions", or votes, in the Senate since Mr Turnbull's elevation to the Liberal leadership in September.
The Greens support for coalition divisions is up 13 per cent, while Labor's is up six points.
Crossbench senators Glenn Lazarus, Ricky Muir, Dio Wang, John Madigan and Jacquie Lambie have all been more likely to vote with the government.
However, independent Nick Xenophon, Family First senator Bob Day and Liberal Democrats senator David Leyonhjelm are now less inclined to back the coalition.
The study found 43 per cent of divisions had been won with Labor backing the Turnbull government, while 35 per cent were won with crossbench backing.
The government has lost 35 per cent of all divisions in the Senate since September 7 - down from 39 per cent under Mr Abbott.
