Motorists caught speeding just above the limit could get a reduced penalty under proposals for fairer fines.
Fairer fines will not apply in areas near 'vulnerable' road users
Transport Secretary Alistair Darling has announced a consultation on the government proposals.
Fines could range from £40 and two penalty points for lesser offences up to £100 and six points for the most serious examples of speeding.
Motoring groups said most drivers would welcome the plan, but that the circumstances of each offence should be considered.
The lower penalty would not apply to people speeding in 20mph speed limit areas such as school areas and hospitals.
The changes will replace the 'one-size fits all' approach, Mr Darling said.
"We want to ensure the level of the penalty fits the severity of the offence - including a crackdown on the most dangerous offences," he said.
"The police would continue to enforce speed limits rigorously and motorists will always need to be aware that speeding is highly dangerous and if they are caught they will face a fine, points... and disqualification if they persist."
The consultation includes police plans to hold "speed awareness courses" nationwide, after successful trials by several forces.
These would be offered to first-time offenders in the lesser speeding category - at their own expense - instead of the two-point penalty.
Currently, drivers get a £60 fine and three points for each speeding offence.
Once they accumulate 12 points, they are liable to be disqualified.
Robert Gifford, executive director of the Parliamentary Advisory Council for Transport Safety, told BBC Radio 4's Today programme the government was sending a mixed message to motorists.
"On the one hand the government says 'speed kills' ... but on the other hand it's okay to speed a bit," he said.
He said a vehicle's speed when it struck a pedestrian determined whether they suffered injury, which made it just as dangerous for drivers to creep above the speed limit as exceeding it by a wider margin.
"The penalty should match the risk," he said.
Mary Williams, head of the road safety group Brake, said: "This is pandering to the pro-speeding lobby and is in breach of the government's duty of care to communities.
"This sends a totally wrong message out to drivers, many of whom do not understand the killing power of increased speed."
But Andrew Howard, the AA's head of road safety, said the plan would not alter the danger to pedestrians.
"I don't think the person who slips accidentally over a speed limit is going to be less deterred by two points than he would be by three," he said.
"I think there'll be a much bigger threat there for the person who wilfully disobeys speed limits," he told BBC Breakfast.
He said many drivers who slipped over the speed limit were "distressed and mortified" at having a criminal record.
The RAC said most motorists would back the plan, but urged the government to take the circumstances of speeding offences into consideration.
RAC spokeswoman Rebecca Bell said: "Who's to say that travelling 10mph above the speed limit on a dual carriageway late at night is a more serious and dangerous offence than going 5mph above the speed limit outside a school?"
"We will need to take speed and circumstance into consideration if these plans are to work sensibly."