Ordinary household and construction debris is welcome. The limits come from the state's landfill rules and from what the city landfill will take at the gate.
New Mexico's solid waste rules keep several categories out of a regular landfill. Lead-acid batteries, like the ones in cars and trucks, are barred. So is regulated hazardous waste, infectious medical waste, and radioactive material.
Clovis adds its own list. The city makes it unlawful to set out, or carry to the landfill, any waste oil, used engine oil filters, liquid paint, paint thinner, or solvents. Household amounts of waste oil and paint are accepted when you bring them to the landfill on their own, but they cannot ride along loose in a container.
Liquids of any kind, fuel, propane tanks, and asbestos also stay out of a standard dumpster. Tires and large appliances are handled separately, so mention them when you book rather than tossing them in.
One more thing worth planning for: loads have to be covered and secured on the way to the landfill, and the city charges more for an unsecured load. If you are unsure about an item, ask your account manager before it goes in.