Soot!

My suggestion differs from other soot suggestions somewhat. Instead of being left behind by items burned in fires or as a deliberately smelted block, any item burnable as fuel (that doesn't already produce a unique recipe) placed in the smelting slot of a Furnace should be smelted into Soot. Sticks, Bows/Crossbows, Coal (but not Coal Ore) would be consumed in the process while also consuming fuel at the normal rate.

Soot and this process of creating it can have uses for many different kinds of Minecraft Players:

• For PVPers, Soot could be used as a brewing ingredient - soot is caustic and can be used to create a kind of Soap, so maybe it crafts a "Soap Potion" that removes some debuffs when consumed/splashed.
• For Builders: in the upcoming Caves update, this caustic property could be used to strip any Weathered Copper of its tarnish, should a player want to do so.
• Also for Builders, Soot could be an alternative to ink sacs and wither roses for creating black dye.
• For Redstone, being able to burn away items from certain item pools can greatly reduce the sorting complexity of some farms and contraptions.