Eleven officers who have been convicted of crimes - including eight who have been violent towards women and girls - are still on the Police Scotland pay roll.

In a letter to the Scottish Parliament's justice committee, Chief Constable Jo Farrell said there were other cases with "incontrovertible evidence" against officers, but they cannot be sacked quickly enough.

Farrell also said the £4.5m annual cost of the 80 officers who are currently suspended was down to "sluggish" conduct arrangements, as well as the time necessary for cases to go through courts.

She described the state of affairs as "intolerable" and called for a modernisation of the police conduct regime.

The revelation follows a number of high-profile cases of police officers who have been exposed as rapists this year alone.

Derek McNee, Campbell Petrie, Carmichael John Williamson and Cameron Ross have all been convicted and are no longer on the payroll.

Meanwhile, Alan Greer, who was named as a violent serial rapist by a BBC investigation, took his own life in May after police raided his home.

It also emerged last month that 45 serving officers are currently suspended over allegations of violence against women and girls.

Farrell wrote the letter to justice committee convener David Linden ahead of a meeting this week.

She said: "There are cases of proven criminality where the existing process has taken too long because of sub-optimal regulations.

"This can leave individuals who ultimately have no place in policing within the organisation for longer than they should be."

She continued: "There are other cases where there is incontrovertible evidence against officers which cannot be fast-tracked for dismissal under current arrangements.

"This is intolerable to me, as Chief Constable, and would rightly be intolerable to the public."

That officers remain suspended for years, she said, has a "welfare impact, a cost to the public purse, and reduce policing's overall deployable resource".

Last month, Farrell said that between 300 and 400 officers had now been re-vetted as part of new rules brought in following the murder of Sarah Everard by Met Police officer Wayne Couzens.

The committee will be discussing options that will allow Police Scotland to act quicker in cases where there are convictions.

Farrell said the proposals under consideration would "modernise the police conduct regime, to accelerate hearings for the most serious cases and enhance transparency of outcomes".

"I strongly support the focus on treating witnesses and complainers in a trauma-informed way," she said.

Justice Secretary Neil Gray said: "The Chief Constable is right that cases involving officers convicted of serious offences should be dealt with more quickly.

"This is why we have introduced regulations to Parliament that will allow Police Scotland to act quicker in cases where there are convictions."

He added: "These are aimed at improving transparency and strengthening support for victims and witnesses, while retaining appropriate safeguards."