The Minister for Transport, Mr Brennan, has said he supports a proposal that the speed limit on country roads be reduced from 60 to 50 m.p.h.
He said the speed limits were "silly" and too slow in areas such as the Stillorgan dual carriageway, and too fast in other areas, such as narrow rural roads.
"If people think that speed limits are crazy and silly, they won't obey them. There are some places where they are patently silly. The Stillorgan dual carriageway is one that we all probably know," Mr Brennan said.
Speaking on RTÉ's Morning Ireland, he said he expected to get a report from a Government working group on the issue within two weeks.
The group suggests the new limits should be introduced when the State converts to metric speed measurements.
It recommends an increase in the general motorway speed limit by four miles to 74 m.p.h. and a minor increase in the 60 m.p.h. limit for wide single-lane roads with hard shoulders.
The group suggests a 30 m.p.h. speed limit in urban areas and a limit of almost 20 m.p.h. near schools. "I do support the broad thrust of them [the recommendations]," Mr Brennan said yesterday.
The Department of Transport aims to have metric speed limits in place by next summer.
Mr Brennan said the penalty points system had made a significant difference to driver behaviour, as some people only began to spot the anomaly in speed limits after penalty points were introduced.
Almost 44,000 drivers have now received penalty points since the system was introduced almost 10 months ago.
Up to last week one driver in the Dublin area was still on 10 penalty points, while four had received eight points each. Drivers will receive a six-month disqualification when they reach 12 points.
The computerisation of the penalty points system is still being worked on, a spokesman for Mr Brennan said yesterday. The new programme was due to be tested in the coming months and should be in place by next summer, he said.
The Automobile Association has welcomed Mr Brennan's support for speed limit changes. Its spokesman, Mr Conor Faughnan, said erratic and eccentric speed limits peppered the road network, and it was difficult for drivers to adjust to them.
The proposed 50 m.p.h. speed limit would be the biggest adjustment for drivers, he said.
Meanwhile, the Motorcycle Action Group (MAG Ireland) has repeated its call for training for all new road-users, following Mr Brennan's announcement of mandatory training for young motorcyclists.
"Twenty per cent of all fatal accidents are motorcyclists, and when you consider that motorcyclists only account for 2 per cent of the vehicle population, you can see that it is horrendous," Mr Brennan said yesterday.