Most household and construction debris is fine. Nebraska's landfill bans and the City's own disposal rules set the limits.
The Nebraska Department of Water, Energy, and Environment lists several items that are banned from every landfill in the state. These include waste tires in any form, waste oil, car batteries, and household appliances like washers, dryers, water heaters, refrigerators, and stoves.
Yard waste has a seasonal rule. From April 1 through November 30, leaves and grass clippings can't go to a Nebraska landfill, so keep them out of your container during those months.
The City's disposal sites also refuse liquid waste and sludge. Hazardous waste, paint, solvents, and fuel can't go in a standard dumpster, and asbestos needs special handling.
If you're unsure about any item, ask your account manager before it goes in.