Normal remodel and cleanout debris is fine. The limits come from Mississippi Department of Environmental Quality rules and from what the City of Pearl refuses at its own sites.
The state keeps a long list of material out of sites that take construction debris. Household garbage and food waste belong elsewhere. So do liquids, sludges, and contaminated soil, along with paint, paint buckets, oil containers, and chemical containers. Engines, motors, whole tires, and batteries of every type are out, and so are refrigerators, air conditioners, and medical waste.
Hazardous waste, solvents, fuel, and asbestos never belong in a standard container either.
Pearl adds its own refusals at the compactor station: tires, fuel containers, flammable liquids, tree limbs, paint, and computers are turned away there. City sites also refuse oil, livestock carcasses, vehicle bodies, and wire longer than four feet.
One stray paint can is enough to hold up a whole load, so set those items aside and ask your account manager where they should go.