Most construction and household debris is fine to load. The limits come from Delaware's disposal rules and the policies at state disposal sites.
Delaware's Department of Natural Resources and Environmental Control says yard waste may not go in your trash or in Delaware landfills. Grass, leaves, and brush should be composted or recycled instead.
The state also treats five items as universal waste, a type of hazardous waste with its own handling rules: batteries, mercury-containing equipment, old farm pesticides, lamps such as fluorescent bulbs, and aerosol cans. Keep them out of your container.
Hazardous waste, liquids, paint, solvents, and fuel can't go in a standard dumpster either. Asbestos needs special packaging, paperwork, and an appointment at the landfill, so it can't ride in a regular load. Tires are charged at a higher rate by weight, so mention them when you book.
If you're unsure about anything, ask your account manager before it goes in.