Most renovation and cleanout debris is fine. The limits come from North Carolina's landfill bans and from what the City's transfer station accepts.
North Carolina keeps a long list of items out of landfills. That list includes used oil, antifreeze, lead-acid batteries, whole tires, oil filters, large appliances, and yard waste. It also covers TVs, computers, monitors, and printers, plus aluminum cans and some plastic bottles. Mercury bulbs and thermostats can't go to construction debris landfills either.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either.
The City's transfer station also refuses medical and radioactive waste. For paint, gasoline, motor oil, car batteries, and electronics, Durham residents can use the free Household Hazardous Waste Center on East Club Boulevard.
If you're unsure about an item, ask your account manager before you load it.