Drivers caught speeding could escape fines and penalty points by doing a course on the dangers of fast driving.
Attempts to tackle speeding are diversifying
The change could help overcome drivers' resentment of speed cameras, hopes the Association of Chief Police Officers.
The choice will apply for first time offenders in England and Wales speeding by less than nine miles an hour.
Road safety charity Brake welcomed the extra driver education but said it should not replace any penalties.
BBC crime correspondent Neil Bennett said: "Senior [police] officers want to take some of the heat out of the debate on speed cameras.
"Some motorists suspect they are just a means of raising money for the police."
Drivers in a 30mph zone doing up to 39mph will be given the opportunity to go on a speed awareness course if it is their first offence.
It will last one day and be run by local councils.
The cost of the course will be borne by the motorist and roughly the same as the potential fine. No penalty points will go on the licence.
In a pilot scheme in Lancashire, the vast majority of those caught opted to go on the course.
Mary Williams of Brake welcomed more education on the dangers of speeding but said any course must be only an added extra.
"We think education is really important," she said. "However the point of points is eventually to ban drivers who are not fit to be on the road.
"If you are having an education scheme, it must be an 'and' rather than an 'or'."
She said people's resentment towards speed cameras was a "bit of a myth".
"We know from public surveys conducted by the government and us that the majority of people do accept speed cameras as an important enforcement device.
Changing someone's attitude may not go on to alter their behaviour, she said.
She added there needed to be more education on the danger of rural speeding, not just in towns and cities, "because that is where most vehicle occupants die in head on collisions or overtaking manoeuvres".