Three options were presented to Cabinet as part of the Government's regular review of the quota - leaving the annual quota at 750, increasing it to 1000, or doubling it to 1500.
The decision was made to increase it to 1000 and announced by Woodhouse and Prime Minister John Key in June.
A June 3 Cabinet paper outlines cost estimates for the "increase" options.
Moving the quota to 1000 would cost an extra $20.6 million a year from 2020/21, according to the document.
Taking the bigger step to double the quota would cost $41.2 million a year from 2020/21 - a difference of $20.6 million.
Any offset in additional tax revenue generated by refugees was not estimated.
Woodhouse has cited cost and logistics as a reason why doubling the quota was decided against.
He also wanted to leave capacity for "another emergency like Syria" and for the potential growth of a scheme which allows non-government groups to resettle refugees at their own cost.
Modelled on a Canadian programme, that new scheme will begin with 25 refugees next year but could be expanded if it is successful.
A spokeswoman for Woodhouse said decisions on how big the scheme could grow had not been made.
But a March 7 briefing from the Ministry of Business, Innovation and Employment (Mbie) to Woodhouse included a proposal to, from 2018/19, approve a new 250-a-year category of "outside the quota" refugees that would be supported by community groups.
New Zealand church leaders have said they have capacity for an additional 1000 refugees a year.
The same Mbie document analysed risks relating to proposals including an increase in the refugee quota, and "noted the example of a mass arrival as something that could cause a spike in [UN] Convention refugee numbers".
In the event of a mass arrival - a group of 30 or more asylum-seekers - consideration would be given to the quota programme being temporarily suspended, the document states.
In May last year a boat of asylum seekers carrying 65 people set off from Indonesia, with those on board saying they hoped to reach New Zealand.
The boat was turned around by Australian authorities - a move which later sparked controversy after allegations payment was made to people-smugglers.
Prime Minister John Key said at the time he had been advised the boat had a credible chance of making it to New Zealand - something rubbished by Labour leader Andrew Little, who accused Key of beating up the issue as a distraction.
A law change in 2013 gave the Government greater powers to manage a mass arrival of asylum seekers. In that event, the Government has power to detain arrivals for up to six months. This detention could be extended by 28 days with approval from a judge.
