Talks with other devolved leaders were held at Downing Street.
Courses For Speeding Considered
Drivers caught just over the speed limit could be sent on educational courses as an alternative to prosecution under plans being considered by the Scottish Government.
The move was revealed in a letter from Transport Minister Derek Mackay to Conservative justice spokeswoman Margaret Mitchell.
The Conservatives had called for ministers to consider introducing speed awareness courses of the kind used in England and Wales as an alternative for motorists at the lower end of the speeding scale.
In a letter to Ms Mitchell, Mr Mackay said: "I support the concept of offering driver education as an alternative to prosecution where appropriate.
"Consequently, one-day 'Driver Alertness' and 'Ride' courses, tailored to car drivers and motorcyclists respectively, are currently available to the prosecuting authorities where the level of offence would normally attract a fixed-penalty notice.''
Mr Mackay said evidence is being sought to see whether speed awareness courses would be appropriate in Scotland.
Welcoming the news, Ms Mitchell said such a scheme would result in a "fairer system which prioritises safer driving''.
She said: "Given the increase in traffic convictions, it is surely time to consider an alternative for those who are not significantly over the speed limit.
"Offering speed awareness courses would be a more effective alternative to points and a hefty fine.
"Involvement in such a scheme is aimed at helping improve safety by promoting better driving behaviour.
"In addition to this, motorists - many of whom rely on their car for work and family - consider they are being disproportionately targeted by overzealous crackdowns.''
A Scottish Government spokesman said: "The Road Safety Framework contains a commitment to consider whether the introduction of a speed awareness course would be appropriate for Scotland.
"We are currently taking this forward with key partners such as COPFS (Crown Office and Procurator Fiscal Service), Police Scotland and the Safety Camera Programme.
"There is general support amongst our road safety partners that we should enhance the existing evidence base by introducing a pilot scheme in Scotland.
"However, there is still a great deal of work to be done in terms of agreeing the scope of a pilot.''
Stefano Brizzi is accused of murdering the Scottish police officer.
It happened in the Govanhill area at lunchtime.
It's being treated as attempted murder.
Most Viewed Pictures On Heart
Recently Played Tracks
To listen live, choose your preferred location:
Deposit £10 to get a £40 Welcome Bonus - That's £50 to play bingo, slots and more!*
Over 50 tracks to make you feel-good. New album out now...
Find your local four day weather report here.
Make Heart the soundtrack to your day and you could be a winner with great prizes up for grabs throughout the day.
Find out more about some of the companies advertising on Heart Scotland- East.