Most construction debris and household junk can go in your container. The limits come from Texas rules that apply to every municipal landfill in the state.
The Texas Commission on Environmental Quality bans these items from landfills: lead-acid batteries, used motor oil from home oil changes, used oil filters, whole tires, and refrigerators, freezers, or air conditioners that hold refrigerant. Liquid waste, regulated hazardous waste, PCB waste, and radioactive materials are banned too.
Tires have one exception. The state allows tires in a landfill only once they've been split, quartered, or shredded, so whole tires need to stay out of your dumpster.
Paint, solvents, fuel, and asbestos can't go in a standard dumpster either. For household chemicals and electronics, the City of Fate offers a doorstep hazardous waste pickup on the first Tuesday of each month, which you schedule ahead of time.
If you're not sure about an item, ask your account manager before you load it.