NSW Police Assistant Commissioner Mark Jenkins, who took command in the final hours of the December 2014 siege, returned to the witness box on Monday where he was thoroughly interrogated over the decision to continue with the reactive strategy of "contain and negotiate" with gunman Man Horan Monis.

Among the briefing notes taken by Assistant Commissioner Jenkins' personal scribe shortly after he assumed command around 10pm on December 15 was a description of the hostages as "moving around freely, jovial, casual, going upstairs freely".

Seizing upon the word "jovial", counsel assisting the coroner, Jeremy Gormly, SC asked the Assistant Commissioner to elaborate on the factors that led police to conclude the hostages were in a situation of joviality and casualness.

"That appears to be information provided to you during the course of the evening?," Mr Gormly asked.

"Yes," Assistant Commissioner Jenkins replied.

"It is a remarkable word in the context, isn't it?", Mr Gormly asked.

"It would appear to be yes," Assistant Commissioner Jenkins said but added he did not recall the word being used.

"I don't recall the exact conversation. It was obviously part of the briefing that was being provided to me where the tactical adviser was telling me the hostages were being allowed to move around freely and casually, which is unusual in a siege-hostage situation."

The inquest has previously heard evidence from some of the 18 hostages who described their terror across the 16-hour ordeal, which ended in the execution of Tori Johnson by Monis at 2:13am on December 16. Hostage Katrina Dawson was killed by an errant police bullet, as police stormed the cafe moments later.

Assistant Commissioner Jenkins also conceded he did not recall Man Monis' name when he was identified as the gunman, despite Monis' extensive criminal history and his involvement in Monis' bail decision one year earlier.

Last year, Assistant Commissioner Jenkins told the inquest of his regret at not asking the state's prosecutors to appeal the decision of the Penrith Local Court in December 2013, in which gunman Man Monis was granted bail on charges of being an accessory to the murder of his wife.

"Certainly the name Monis was brought to my attention mid afternoon by some of my investigators but i'm not sure if they briefed me exactly on what he'd been charged with previous at that stage."

He told the inquest he had been "generally aware of the name" but "whether I associated those particular offences with Monis when I was told that name on that day, I'm not sure."

After he had assumed the command post, he was given a police profile on Monis, which contained a photograph and details of the alleged murder and sexual assault charges against him.

Despite Monis' history of alleged violence, Assistant Commissioner Jenkins said the profile did not add to any concern about the risk he proposed.

Instead, he took a "a little comfort" from the fact that the murder offences were undertaken by a third party and "perhaps he wasn't violent himself," he said.

Assistant Commissioner Jenkins defended the decision to continue with the contain and negotiate strategy after he assumed the command post, even though police negotiators had failed to speak directly with Monis more than 12 hours after the siege had begun.

He said the terrorist component of the siege "brought very little new" to the physical management of the situation, describing the contain and negotiate strategy as "applicable in this type of situation as it would be in a domestic situation".

Asked whether, with the benefit of hindsight, a terrorism-related siege should be managed differently from a family dispute siege, Assistant Commissioner Jenkins he "haven't given that a lot of thought."

"That would require policy changes and legislative changes, no doubt," he said.

The inquest continues before NSW State Coroner Michael Barnes in Sydney.