Figures show that over the past four years, the council has taken 10 calls complaining about a traffic cone on the Duke of Wellington statue, one of Glasgow's most photographed sights.
It emerged last year that the council spends £10,000 a year removing cones from the statue outside the Gallery of Modern Art - which itself sells postcards featuring the cone-crowned landmark.
The local authority received seven complaints in 2010, two in 2011 and just one in each of 2012 and 2013. Complaints peaked in 2009, when 28 calls were taken.
In November, last year, the council threatened to spend £65,000 elevating the statue to stop pranksters crowning it with traffic cones. But the proposal was met with fury from cone fans, including comedian Greg Hemphill, who called on social media for the plan to be scrapped.
Graeme Hendry, SNP leader on the council, said: "To pick a £10,000 fight with a traffic cone when we have many roads and pavements in awful condition shows some pretty mixed-up priorities from the council."
A council spokesman said: "Putting cones on the statue may seem harmless, but a fall from that height could be very harmful.
"We would urge anyone considering putting a cone on the statue to not do so."