In a draft document written for Senator Cash, the government's public service minister, the commission briefed her on union claims about the enterprise agreement and the likely support for the deal from staff.

Three ballots ended in massive rejections of the agreement before the dispute entered the industrial umpire for arbitration, where lawyers are battling over the role of the Coalition's new workplace bargaining rules in the failure of negotiations.

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The stoush remains complicated also by the 2015 merger of the Department of Immigration and Border Protection with the customs service, and the different conditions in their previous workplace deals.

In an email tendered to the Fair Work Commission this week, Immigration department assistant secretary David Leonard sent changes his agency made to the briefing back to the public service commission, detailing Immigration's positions in response to claims from the Community and Public Sector Union.

"Customs employees have long enjoyed generous terms and conditions, many of which are beyond what is common in the APS. It is these conditions which the CPSU has based its claims around," the draft briefing said, before describing Immigration's position.

CPSU national secretary Nadine Flood claimed documents received by Fair Work showed Senator Cash used the APSC, a body set up to uphold public service values, to work out whether agreements could be pushed through by identifying thousands of Immigration workers to "do over" and get a bare 51 per cent vote.

A Coalition spokeswoman described the union's claims as "not correct and not credible".

"The role of the APSC is to assist departments and agencies to apply the government bargaining policy, which applies to all negotiations," she said.

"The minister plays no role in this process.

"The single biggest impediment to new agreements being made and public servants receiving a pay rise has been the attitude of the CPSU, which has unsuccessfully opposed the application of the bargaining policy and sought to prevent new agreements being made across the public service."

The public service commission discussed bargaining strategy and possible vote results with the Immigration department during the four-year workplace fight, the documents show.

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In emails to the commission, Immigration officials estimated the size of the possible 'no' result, said the commission had canvassed resuming talks with a new, more appealing offer that could win majority support, and discussed a plan to coordinate a vote with ballots at agencies.

Public service commissioner John Lloyd said it routinely gave agencies bargaining advice, including on strategy, as they shared a "mutual interest" in reaching new agreements that kept to the government's workplace policy.

One email in July 2015, before the first failed Immigration ballot, said the public service commission did not want a ballot if the agreement was heading towards defeat and that it was "interested in exploring options for going back to the negotiating table with a refined offer that could be more appealing for the workforce and more likely to receive majority support."

In another email, sent in the lead-up to the third ballot, an Immigration official suggested a change to its agreement that would win additional "yes" votes and asked for the commission's "input" while noting the APSC had previously not supported the concession.

"We are at a potentially delicate point with this third ballot, where we believe that we may be approaching around 50/50 views in our staff population so an extra 1000 votes would potentially make a material difference to a ballot outcome," she told the commission.

Mr Leonard at a Fair Work hearing on Wednesday denied the public service commission had shaped the agreement on matters outside the government's bargaining policy.

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