Traffic was flowing faster today after tolls were scrapped at midnight on two major Scottish road bridges.
But the increase in speed was only marginal - and may have been mainly caused by school holidays, they said.
The assessment came from a traffic information service, keepmoving.co.uk, after tolls were scrapped on the Forth and Tay bridges.
A spokeswoman for the website said that as tolls on each bridge applied only one-way, into Fife, little difference would have been expected in the morning peak as most traffic crossed from Fife into Dundee and Edinburgh.
Edinburgh schools were also on half term this week, with Fife schools on holiday at the end of this week, she said.
"Having said that, and with only one day to compare, the typical speed across the Forth Bridge this morning was an average 10mph compared to around 8mph last Monday," she said.
"The Tay Bridge registered an average 13mph today and around 10mph last week, so some slight improvement, but mainly attributable to school holidays."
Transport minister Stewart Stevenson signed an order last month marking the end to more than 40 years of fees for people in Fife, Tayside and the Lothians.
Since the bridges opened in the 1960s motorists have paid £1 for cars on the Forth bridge and 80p on the Tay.
Supporters say scrapping the tolls will ease traffic congestion but environmentalists claim pollution levels will rise.
The new legislation was among the first brought by the new SNP administration, and several MSP marked the occasion by being the first to cross the Tay Bridge toll-free.
The National Alliance Against Tolls (NAAT) said: "It has been a long fight to remove the tolls and we are delighted that Scotland will again be a toll-free nation.
"This will not only be a boost for the immediate area of the tolls, it will also enable Scotland as a toll-free nation to attract more inward investment and tourists."
More than 22 million vehicles cross the Forth Bridge each year, making it one of the busiest estuarial crossings in the UK.
The original construction costs were paid off in December 1993 but since then tolls have funded the bridge's maintenance and improvements.
The Forth Estuary Transport Authority and Tay Road Bridge Joint Board remain responsible for managing the bridges.
They will receive money direct from the Scottish Government.
The Tay board is also getting a one-off grant of £14.8 million to allow it to repay all outstanding loans.
Work to remove tollbooths on the bridges began last week.
Tolls on the Skye Bridge were abolished in December 2004 and on the Erskine Bridge in May 2006.
Environmental group WWF Scotland said the scrapping of the tolls would only add to the global problem of climate change through an increase in traffic levels.
Acting director Dr Dan Barlow said: "On economic, social and environmental grounds there is simply no justification for scrapping these tolls.
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