Most remodeling and cleanout debris is welcome. The limits come from Rhode Island law and from what the state facility will take at the gate.
Keep out hazardous waste, liquids, paint, solvents, fuel, used oil and asbestos. Rhode Island also runs separate statewide routes for electronics, tires, car batteries and mattresses, which means those items have to travel on their own rather than buried in a mixed load.
Televisions, monitors and computers are the usual culprits. One set tucked under a pile of drywall can get a whole container turned away, so pull them out before loading starts.
The City's own crews will not take renovation debris at the curb either, which is exactly why a container makes sense. The City disposal guide says the property owner is responsible for getting construction, demolition and renovation material to the state facility.
If an item has you unsure, ask your account manager before it goes over the rail.