Most household and construction debris is fine in your container. Mississippi's landfill rules and the regional landfill decide what isn't.
Mississippi keeps a longer list than many states for sites that take construction and demolition debris. Those sites can't accept paint, paint buckets, oil containers, or chemical containers. Engines, motors, whole tires, and all types of batteries are banned too, along with liquids, sludges, and contaminated soils.
Landfills in Mississippi also have to screen out hazardous waste, PCB waste, bulk liquids, and asbestos that isn't properly bagged. Whole tires deserve special care, since the state can fine anyone who dumps a waste tire illegally, and each tire counts as a separate violation.
Fuel, solvents, pressurized tanks, and medical waste are never allowed in a standard dumpster. Mention tires and appliances when you book.
If you're unsure about an item, ask your account manager before you load it.