Most construction debris and household junk is fine. The limits come from Minnesota law and from what the receiving site will take.
State law keeps a specific list out of the city's own collection system, and the same items do not belong in a rented container either. That list covers batteries, chemicals, fluorescent light bulbs, household cleaners, oil based products, paints, tires, and treated lumber. The city publishes it alongside its drop-off directions.
Hazardous waste, liquids, solvents, fuel, used oil, and asbestos cannot go in a standard container anywhere in the state. Asbestos has its own route through the county, and it must be wetted and bagged before it is accepted.
Electronics have a separate path as well. Computers, televisions, and monitors are taken at designated drop-off sites rather than mixed into a load.
It also helps to know what counts as demolition waste here, because the city's definition is wide. It covers metal, concrete, glass, wood, asphalt, insulation, brick, mortar, wire, conduit, pipes, and plumbing and lighting fixtures, plus anything state law treats as hazardous. Clean sand, gravel, earth, rock, sod, and boulders are treated as clean fill instead. If an item has you guessing, ask your account manager before it goes in.