The battle over the legality of the Australian Federal Police's search of the union's Dickson headquarters in August wrapped up in the ACT Supreme Court on Wednesday, following three days of hearings.

Acting Chief Justice Richard Refshauge has now reserved his decision in the case, and police have urged him to do all he can to make a speedy decision.

The AFP are still sitting on roughly 10,000 documents seized from the Construction, Forestry, Mining and Energy Union's ACT headquarters, but an injunction is preventing them from inspecting or using the material.

The CFMEU are arguing police did not comply with their legal requirements during the lengthy operation, and are pushing for documents to be returned or destroyed.

The raid went for 13 hours, and police were forced to apply for a second warrant to continue the search, because the first expired.

The granting of the second warrant, which police sought to prevent union officials from destroying documents, is one of the issues put under the microscope in the ACT Supreme Court this week.

The union's barrister Peter Morrissey, SC, argues there was no evidence to back up police's fears that ACT officials would destroy material. He said they had been wholly cooperative in legal proceedings up to that point.

In justifying their fears to the magistrate granting the warrant, police used interim findings of Trade Union Royal Commissioner Dyson Heydon that a pervasive culture existed within the broader, national CFMEU body.

Mr Morrissey has argued that finding had no connection with the potential destruction of material by ACT officials, and was only an interim finding.

But the AFP's barrister Andrew Berger argued on Wednesday that other probative information had been available to the magistrate when she decided to issue the second warrant.

Mr Berger said the AFP could not provide that information to the ACT Supreme Court because police did not want it to make it publicly available.

That prompted concern from Justice Refshauge.

"I am loathe to decide a matter that goes to the coercive interference with the rights of citizens on the basis of some secret information which [I] can't see," he said.

"[The magistrate] had the full monty, some of that is secret and can't be made publicly available."

The legality of the raid is also being contested by he union on a range of other grounds.

It argues its members were deliberately restricted from observing police as they searched, that the warrant wasn't given to officials to read as soon as practicably possible, and that copies of the seized documents were not provided.

The AFP argues the breaches, if proved, were technical in nature and should not see the withholding of evidence of potential criminality.

Justice Refshauge will hand down his decision at a later date.