Construction debris is its own category of junk for one big reason: weight. A pickup bed of drywall scraps outweighs a room full of furniture, and disposal sites charge by the ton. That single fact explains most of what follows.
Weight is the whole ballgame

Furniture and boxes price by volume — how much truck they fill. Demo debris prices by weight and handling: shingles, tile, plaster, and concrete are dense, and a small pile can out-cost a big one. Estimates that see the material in photos beat estimates that hear it described.
Mixed loads cost more than sorted ones. Clean drywall in one pile, lumber in another, and metal separate turns one expensive mixed ton into cheaper sorted material — some of it, like scrap metal, worth actual money.
What can and can't ride
Standard remodel output hauls fine: drywall, lumber, cabinets, flooring, tile, fixtures, roofing. The refusals are consistent everywhere: liquid paint, solvents, asbestos-suspect materials (pre-1980 flooring and insulation deserve testing before demo), and tires.
Around Knoxville, latex paint dries into disposable solid with cheap hardener; oil paint and solvents wait for a household-hazardous-waste event. Asbestos is the one to take seriously — abatement is a licensed trade, not a hauling job.
DIY versus hauled
Knox County's convenience centers take resident loads of many materials, and for a small weekend project with a truck that math can win. It stops winning when trips multiply, when the load needs sorting at the gate, or when your Saturday is worth something — a crew loads, sorts, and disposes in one pass with the receipts to prove it.
Keeping the remodel tidy as you go
Scheduled pickups during a long project beat one monster haul at the end: the driveway stays usable, materials stay sorted, and nothing sits in the rain gaining water weight — which, on a per-ton price, you literally pay for.
Getting the number before the mess
Photograph the pile — or the room about to become the pile — and note anything pre-1980 that demolition will disturb. Those two steps produce a real quote and flag the asbestos question while it is still a question.
Sorted, dry, and photographed is the cheapest condition debris ever achieves; every day it sits mixed in the weather, the per-ton math gets worse.