Most construction and cleanout debris is welcome. The limits come from South Dakota law and from the City landfill's own rules.
South Dakota's natural resources agency says state law has kept four things out of landfills since 1995: yard waste, lead-acid batteries, used motor oil, and white goods, meaning large appliances. The Brookings landfill still takes appliances and yard waste, but it handles them apart from the trash. Appliances with Freon go to a separate area so the coolant can be removed.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. Brookings collects many of those items at its yearly Household Hazardous Waste event, including antifreeze, used oil and filters, wet paint, pesticides, pool chemicals, and fluorescent bulbs.
Stained or chemically treated lumber also has to be dropped in a separate area at the landfill. Mention it when you book.
If you're unsure about an item, ask your account manager before you load it.