Most remodeling and cleanout debris can go in your container. The limits come from Michigan's landfill rules, which every load from South Haven has to follow.
Michigan keeps several items out of landfills. Grass, leaves, and other yard clippings must be composted, not landfilled. Used oil and car batteries have to be recycled, and whole tires can't be buried. Empty drums must be crushed first, and asbestos needs special handling.
Standard dumpsters also can't take hazardous waste, liquids, paint, solvents, or fuel. For household chemicals, electronics, and tires, the Van Buren Conservation District holds collection events for county residents, including one each year at South Haven Public Works.
If you aren't sure about an item, ask your account manager before you load it.