Standard construction and cleanout debris belongs in a roll-off container. What makes Garden City distinctive is how firmly the City keeps that material out of its own trash carts.
The City's prohibited list bars all building contractor materials from City trash containers, along with all concrete, bricks, earth, and sod. It also bars ashes, including fireplace ashes, medical waste from human or animal care, unprocessed animal matter, and tree trimmings thicker than two inches or longer than four feet. In practice, that is the reason a remodel needs a container of its own.
Household hazardous waste liquids are on the same list. Paint, oil, petroleum products, and the cleaners, bug killers, and weed killers that go with them all have to be kept out, and the City runs a facility that takes them instead.
Tires are regulated separately in Kansas, where the state runs a dedicated waste tire program with its own permitted facilities and transporters. Keep them out of the container and mention them when you book.
Asbestos, solvents, fuel, and pressurized tanks stay out of a standard container as well. When an item has you guessing, describe it to your account manager before it goes in.