Most building and cleanout debris is fine to load. The limits come from state rules and from what the city sites will take.
Alabama requires regulated solid waste to go to a permitted landfill, and the state defines that broadly. The Alabama Department of Environmental Management names the list: household trash, furniture, old vehicles, roofing material, other construction debris, and scrap tires. Burning any of it without state approval is not allowed either.
Tires are the item that trips up the most cleanouts here. They hold water, breed mosquitoes, and draw rats and snakes, so the state treats piles of them as a problem in their own right. Keep tires out of the container and mention them when you book.
The state also asks households to take spent lead-acid batteries back to the dealer they came from, and it treats putting any household chemical in the trash as a last resort, with no free liquids allowed. Paint, solvents, fuel, used oil, and asbestos stay out of a standard container.
One useful piece of good news: unpainted concrete and brick, along with stumps, limbs, and leaves, are not regulated the way household and construction waste is. Ask your account manager how to split your load and you may pay less to get rid of it.