* Further restricting the ability of courts to impose fines for non-compliance in court procedure, by clarifying that this can only be done rarely and for significant non-compliance
* Remove the word "substantial" from the "miscarriage of justice" test.
Mr Power had last week tried to garner support for the pre-trial disclosure regime by proposing that the Rules Committee, a panel of legal experts, decide whether to make it mandatory.
But this would have only, at best, given the bill a parliamentary majority of one, and Mr Power wanted broader political support.
"I've gained the support of supply and confidence partners ACT, United Future, and the Maori Party by amending aspects of the bill they were concerned about and have raised with me," Mr Power said.
"Discussions with the Green Party are continuing."
Labour's justice spokesman Charles Chauvel said he would recommend to the Labour caucus to support the bill.
"I'm pleased that the objectionable parts of the bill have been removed.
"I would have preferred for this to have happened during the select committee process, but the main thing is that they're gone.
"On the basis of the minister's undertaking, I'll be recommending to caucus that we support the bill."
The bill also contained a number of other changes that already had broad support, including a new system for categorising crime, and tougher rules for granting name suppression for celebrities.
There are six sitting days in Parliament for the Government to progress the bill through its second reading, committee stage and third reading.