Drivers caught doing 40 to 45mph in a 30mph zone could get six points on their licence under new road safety measures unveiled on Tuesday.
Motoring groups say fines should vary according to the offence
Those who go recklessly over the limit should face tougher penalties, road safety minister David Jamieson said.
But drivers caught going just over the limit could get just two points under a new sliding scale of penalties.
The new Road Safety Bill also raises the penalty for using a mobile phone while driving from £30 to up to £60.
Offenders would also get three penalty points on their licences.
Recent figures from the RAC suggest use of mobile phones while driving has actually increased since a ban on driving with hands-on mobiles was introduced.
Mr Jamieson told BBC Radio 4's Today programme: "What we are proposing in this bill is that the range of penalty points for people who are speeding should be extended.
"So those people who are just over the limit where the police enforces would get two points, but it would go up to six points for these people who are well over the limit."
People travelling at 40 or 45mph in a 30 mph zone would "almost certainly" kill someone in an accident and would face higher penalty points in this bill, Mr Jamieson .
The Road Safety Bill would also allow courts to force the worst drink-drivers to retake their driving tests.
Seriously poor drivers could also be made to go into retraining and the maximum fine for careless driving is increasing from £2,500 to £5,000.
On speeding, the bill allows ministers to say certain vehicles, such as donor organ cars, can exceed the speed limits in emergency situations,
Key road safety measures
Variable speeding penalties
Increased fines for drivers using mobile phones
On the spot fines for foreign drivers caught in breach of traffic laws
Tougher action on accidents caused by driver fatigue
Detection of uninsured drivers through computerised system
Ministers want to cut the number of people killed or seriously in road accidents by 40%, and by half for children, by 2010.
The government says it is half way towards meeting the targets, which are based on the average for the years 1994-1998.
But it says more progress is needed: In 2003, 3,508 people were killed and 33,707 seriously injured on Britain's roads.
Other measures in the bill include:
- Allowing police to take evidence at the roadside from suspected drink drivers
- Closing a loophole which allows offenders who pose a high risk of re-offending to continue driving while medical inquiries are carried out
- Mandatory driving bans on anybody found using a vehicle in a dangerous condition for a second time
- Improving enforcement of European laws on driving hours for lorry and most coach drivers
- Holding trials of motorway rest areas to reduce driver fatigue
The bill would allow the transport secretary to introduce a sliding scale for speeding offences but does not set the details. They will be agreed once the results of consultation on the plans has been digested.
The RAC Foundation said it was important to distinguish between those travelling a couple of miles over the speed limit in a non-residential area away from schools and other dangers, and those travelling at high speeds or in sensitive areas.
But road safety campaigners say downgrading some speeding fines sends out the "wrong message".
Stephen Joseph of Transport 2000 said: "We would like to see higher penalties but starting from the current basis and working upwards not down."
Liberal Democrat transport spokesman John Thurso said the move linked to the seriousness of crimes was a well established principle.
"It is vital that we do not send the message that modest
speeding, in towns in particular, is somehow acceptable," he said.
"It is important to ensure graduation genuinely reflects the risks
posed to other road users."
The move is also being seen as an attempt to deflect anger about speed cameras.
The Conservatives have pledged to review all speed limits, assess the effectiveness of all speed cameras and make speed limit signs much clearer.
They have also promised to concentrate on criminals in cars rather than on cameras and to clamp down on uninsured drivers and anti-social behaviour.