Figures show that over the past four years, the council has taken 10 calls complaining about traffic cone which is regularly placed on the Duke of Wellington statue, one of Glasgow's most photographed sights.
The council revealed earlier this year it spends £10,000 a year of taxpayers' cash removing cones from the statue, outside the Gallery of Modern Art in Royal Exchange Square - which itself sells postcards and greetings cards featuring the cone-crowned statue.
Figures, obtained by the Evening Times, show the local authority received seven complaints in 2010, two in 2011, one in 2012 and one last year.
One of the logged complaints, relating to the gallery's selection of cards, says: "GoMA getting grief about this..."
Complaints peaked in 2009, when 28 calls were taken, including three on the same day.
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 and TV and radio presenter Kaye Adams, who took to social media sites in their thousands, calling for the plan to be scrapped.
Politicians also rushed to the defence of the coned statue, urging the council to back down.
Campaigners were delighted when the local authority caved in less than 12 hours after the "Save The Cone" internet campaign began.
In one complaint, logged on May 28 this year, the caller complained that the Duke was wearing not only a traffic cone but a bib and a mask.
On May 7 2010, the council received two complaints that the Duke's face was covered by a mask of Kiss frontman Gene Simmons. On the same day, a similar mask turned up on the Donald Dewer statue, outside the Royal Concert Hall.
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.
"They should show some common sense and just leave the cone up instead of wasting money like some kind of over zealous control freak."
The statue, sculpted by Italian artist Carlo Marochetti, was erected in 1844 to mark the Duke's long military and political career.
Over the years students and other revellers have placed an orange traffic cone on Wellington's head, making it an almost-permanent feature of the statue.
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."