Most building and household debris loads with no trouble. The limits come from Idaho's rules and from what Bonneville County will take at the gate.
Idaho treats dumping waste on public land or at an unpermitted site as illegal, so every load has to reach a facility that is cleared to accept it. The state leaves hazardous material out of the regular trash stream, which rules out solvents, fuel, waste oil, lubricants, pesticides, and wet paint. Liquids and asbestos stay out too.
The county adds its own list. The Bonneville County Transfer Station turns away electronics of every kind, including computers, monitors, printers, and anything holding a lithium-ion battery. The Hatch Pit takes no asbestos at all, and any demolition load needs paperwork showing it is clear of asbestos before it arrives. The Hatch Pit also refuses household trash, carpet, mattresses, furniture with fabric, tires, batteries, paint cans, and fuel containers. The county can inspect any load and reject part or all of it.
Tires, appliances with freon, and mattresses all carry their own handling at the county, so call them out when you book. If an item has you guessing, ask your account manager before it goes in the container.