Most household and remodeling debris is welcome. The limits come from Minnesota law and from what the receiving facility is allowed to take.
Minnesota bans yard waste from the garbage. Leaves, lawn cuttings, weeds, shrub and tree waste, and prunings all have to go somewhere else, which is why brush and branches travel separately from a mixed container.
Household hazardous waste is out as well. That covers paint, solvents, fuel, pesticides, pool chemicals, and anything labeled flammable, corrosive or toxic. Anoka County keeps those out of the trash because they can harm collection crews and the environment. Asbestos stays out too.
Tires, used oil, oil filters, antifreeze, fluorescent bulbs and household batteries all have their own route here through the City's own recycling center. Appliances and electronics need separate handling as well. When an item has you second guessing, ask your account manager before it goes over the rail.