If you want to really clean up the discolored look of those old oak staves, try using Oxalic Acid.
Also known as wood bleach. Comes in crystals, dissolve in water, then spread onto wood surface.
Use gloves...very caustic.
....it'll save you a LOT of sanding.
Oxalic Acid
"Oxalic acid is unique in that it will remove a certain type of stain formed when iron and moisture come into contact with tannic acid in the wood. Some woods like
oak, cherry and mahogany naturally
contain a high amount of tannic acid and a black stain is formed when the wood gets wet with water (tap water contains iron as a trace mineral). A wet glass or leaky vase left on these woods will produce a black ring. Nails and screws will form black rings around the head if the wood gets wet. If tap water is used to wet unfinished oak and mahogany, small gray spots may form on the surface of the wood.
Oxalic acid will remove this discoloration without affecting the natural color of the wood.Oxalic acid is also used to lighten the graying effects of outdoor exposure. It is the ingredient in most deck "brighteners". Used on furniture that has been stripped for re-finishing,
it will lighten the color and re-establish an even tone to the wood, particularly oak."
http://www.antiquerestorers.com/Articles/jeff/using_wood_bleach.htm