The changes mean more drivers would be offered the option to do a speed awareness course Most police forces in England and Wales have adopted new speeding rules that allow drivers to do up to 86mph and avoid points on their licence.
The guidelines mean motorists can pay to do a speed awareness course instead if they are caught at up to 10% above the limit plus 9mph.
Police leaders said 37 out of 44 forces had signed up to the new framework.
Critics say the rules are simply a money-making exercise and allow motorists to break the law.
Previously, only those only those travelling at up to 10% above the limit plus 6mph could be offered one of the courses.
But the amendments were agreed by chief constables at a meeting of the Association of Chief Police Officers (Acpo) in January.
For a 30mph zone, the upper limit for a speeding course would be 42mph.
This would rise to 86mph for motorways and other major roads, although the official limit remains the same.
Acpo said the figure at which a course could be offered was a decision for individual forces, and not all would make it available for higher speeds.
Drivers can only attend one speed awareness course in a three-year period.
Acpo said the increase in courses for drivers had been backed by road safety minister Mike Penning.
The police organisation said the changes would allow more drivers to “undergo an invaluable educational experience rather than receive driving licence penalty points and a fine”.
A spokesman said: “Over recent years, the number of people killed and seriously injured on our roads has fallen significantly, reducing both the toll of personal tragedy and the cost to the public purse.
“This reduction has been achieved through a combination of improved engineering, enforcement and education of which safety cameras are an important element.”
At the start of the month, speed cameras across Oxfordshire were switched back on eight months after they were turned off.
Funding was withdrawn for 72 cameras and 89 mobile sites last August as part of budget cuts in the county.
But police said deaths and serious injuries on the area’s roads went up following the cameras being switched off.
Money for the cameras to be introduced has come from speed awareness courses and backroom savings.
This article is from the BBC News website. © British Broadcasting Corporation, The BBC is not responsible for the content of external internet sites.