The glasses worn by the 9ft tall bronze memorial to Scotland's first first minister have been damaged again, following a similar incident earlier this month.
Police in Glasgow are to study CCTV footage of statue, which stands in Glasgow's Buchanan Street.
The figure was unveiled almost three weeks by Prime Minister Tony Blair.
But within days the glasses had been left twisted and bent by vandals.
Police said that they believed late night revellers may have caused the damage while placing a traffic cone on the statue's head.
Strathclyde Police Supt Robin Howe said: "It has become part of the culture in Glasgow in recent years to place traffic cones on the heads of statues in the city.
"It would appear, however, that the statue of Mr Dewar is not going to withstand this type of prank."
Police who studied CCTV footage put the incident down to high jinks and said they were satisfied that those responsible had no criminal intentions.
Formal complaint
But following the latest incident, Strathclyde Police officers are to study security tapes again to find out how the damage was caused.
A spokeswoman said: "We have not received a formal complaint regarding vandalism of the statue, but it has been drawn to our attention and we will now look at the CCTV footage.
"We are still having to remove people who have been standing on the plinth, trying to get their photographs taken or putting cones on his head."
First Minister Jack McConnell called for those responsible for the last attack to be held responsible for their actions.
A Scottish Executive spokesman said on Saturday: "The First Minister believes that these attacks must stop and that the people responsible should be prosecuted."
A spokesman for Glasgow City Council, which is responsible for the maintenance of the statue, also condemned those responsible.
He said: "We're extremely disappointed that people think that it is amusing to damage this statue and put cones on top of it.
"We hope that the police can catch whoever has caused this latest damage."
The statue was created by 35-year-old artist Kenny Mackay, whose workshop is in Mr Dewar's former constituency of Anniesland.
At the unveiling, Mr Blair said the founding figure of Scottish devolution was "without doubt one of the towering political figures of his generation".