Bedfordshire Police Authority has expressed concern targets for detection of serious violent crime and sexual offences are being missed.
A performance and planning committee heard detection rates for serious sexual offences over the first three months of this year were only 16.5%.
Committee chair Martin Pantling told chief constable Gillian Parker violence needed to be addressed as a priority.
The chief constable presented a report on methods of tackling these offences.
Members welcomed the development of a strategy to deal with serious violence.
Acknowledging that alcohol is often a factor in violent crime, members felt plans to abolish late night opening hours and reinstate traditional pub and club opening hours could save police resources.
They agreed measures were in place that helped police and they recognised that the number of serious violent crimes was not high.
The SOS Bus in Luton town centre on Friday and Saturday nights has helped to reduce demand for police and ambulance or health services, the committee heard.
A dedicated rape investigation unit introduced in 2009 had helped increase the number of cases successfully brought to justice, it was added.
Mrs Parker said the number of sexual offences successfully brought to justice was at 34.4%, above the 32% annual target.
Mr Pantling said: "Violence is a top priority for the police authority.
"We appreciate that the number of serious violent crimes committed is not high.
"But we are disappointed that targets for reducing and detecting the most serious violence are being significantly missed at this point."