It could also be an opportunity to deal with some of the city's other problems causing health and safety issues, she said.
"This sounds a very strange idea of having a posse looking after the city in the small hours getting rid of rubbish, cats, rats and annoying people, [but] I think you could really look into something similar ..."
She clarified that if the group saw people dumping rubbish, she did not recommend they should be shot, but simply stopped.
The student volunteer army might be interested in the work, she said.
"I think this would be very character-building for these young men and women to be out at night cleaning up the city and shooting the occasional cat and rat."
The comments raised a few smiles of disbelief from councillors, including Cr Fliss Butcher, who asked Ms Yeldon if she thought the council should think about putting some money in its next annual plan for a pied piper.
Contacted after the meeting Ms Yeldon said she was serious about all of her comments, including the way to deal with the problems.
The council should at least provide advice to people about dealing with cats and rats, she said.
Planning and environment committee chairwoman Cr Kate Wilson said the committee would be happy to take a look at issues with rubbish perhaps attracting cats and rats.