Most construction and cleanout debris can go in your container. New York State rules and the landfill that takes your load set the limits.
The New York State Department of Environmental Conservation bans burying waste tires in landfills, and its electronics page says New York consumers must recycle many electronic items instead of throwing them out. That covers TVs, computers, and similar devices, so pull them out before loading.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either. The City no longer picks up tires or paint at the curb, so plan for those items separately.
For electronics, Lackawanna residents can use the City Garage on Reddon Street. It takes drop-offs from 8 a.m. to 6 p.m. during the week after each large bulk pickup week.
If you're unsure about anything on your list, check with your account manager before you load it.