Pauley cited "ongoing aspects" of the government's investigation as he directed prosecutors to identify in July what individuals or entities remain subject to continuing probes and explain any need for continued redaction.
Cohen, 52, is serving a three-year prison sentence after admitting a role in paying off two women — porn star Stormy Daniels and a Playboy centerfold Karen McDougal — who claimed they had affairs with Trump. Assuming good behavior, Cohen would be released in December 2021.
Cohen and federal prosecutors said Trump directed the payments. The president denied any sexual relationship with the women and said on Twitter that payments were "a simple private transaction," not a campaign contribution.
The search warrants preceded raids on Cohen's homes and office in April 2018. Media organizations previously persuaded the judge to release much of the material related to the warrants, but not the sections related to the campaign finance investigation.
It remains unclear exactly what part of the campaign finance probe remains unfinished. Cohen admitted that he arranged for American Media Inc., parent of the pro-Trump National Enquirer, to pay McDougal $150,000 to buy and bury her story. He also admitted paying Daniels $130,000 and was reimbursed by Trump's business empire. Both payments came during the 2016 campaign.
Prosecutors said those secret payouts were not reported as campaign contributions and violated the ban on corporate contributions and the $2,700 limit on donations by an individual. Shortly after Cohen's sentencing, federal authorities announced a deal not to prosecute AMI. The deal required the company to admit making the payment to McDougal "in concert" with the Trump campaign to protect him from a story that could have hurt his candidacy.
The non-prosecution agreement was put in jeopardy this year when Amazon CEO Jeff Bezos said the National Enquirer threatened to publish explicit photographs of him unless he publicly declared that the tabloid's coverage of him was not politically motivated.
In April, it was announced that the supermarket tabloid was being sold to the former head of the airport newsstand company Hudson News.