Board members from the trust which runs the hospitals in Carlisle and Whitehaven have been discussing the recent high mortality rates at their facilities.
North Cumbria University Hospitals NHS Trust was highlighted as having 'worryingly' high mortality rates.
A report by Dr Foster, an independent health watchdog, said that the trust was amongst the worst in the country when it came to the number of people dying.
Board members, including interim Chief Executive Ann Farrar, said that progress had already been made when it came to tackling the issue.
They highlighted the results of a new study which they presented to members of the county council's Health Scrutiny Committee.
It shows the Trust's so called 'mortality index' has been steadily declining since the Dr Foster report.