Everyday construction and household debris is fine. The exclusions in Dickinson are written into the City's own definitions and they are unusually specific.
The City treats a list of materials as excluded waste: wastewater treatment plant sludge, petroleum and petroleum products, natural gas products, asbestos, lead, polychlorinated biphenyls, and anything radioactive, volatile, corrosive, highly flammable, explosive, biomedical, infectious, biohazardous, toxic or hazardous. None of that goes in a container and none of it may be set out for collection.
Hazardous waste, liquids, paint, solvents and fuel are excluded on the same basis anywhere in Texas.
Tires and large appliances should be kept separate and mentioned when you book, because they are usually priced per item rather than by weight.
Wet and contaminated material from flood work needs to be described before delivery. It is heavier than it looks and some receiving sites handle it differently from dry debris.
If you are unsure about something, ask your account manager before it goes over the rail rather than after the container is full.