The workpieces in question are a pair of scales for a kitchen knife I'm giving to my son. They're oddly shaped, so my bench vise couldn't hold them, and too thin to hold that way anyway. The ends have been cut off too far from square to use my Time Warp bench dogs; the force of planing would rotate them away from behind the dog and they'd just slide across the bench.
Perhaps I could have rigged up a bird's mouth arrangement with some thin ply, but instead I reached for the woodworker's secret weapon, double-sided tape. This is no ordinary double-stick. It is quite tenacious; in fact you should consider waxing one of the surfaces before laying it down, so you can get it off afterwards.
Mostly I use this tape for machine setups, like temporarily putting a sacrificial fence on the tablesaw, or placing a wooden block on my saw table to prevent my hand from contacting the blade. But once in a while it comes in handy for things like this.
It worked flawlessly. After lapping one face flat on my granite block, I taped the flat face down to a 2x4 scrap and clamped the 2x4 into my vise. In just a few minutes, both scales had two parallel faces, and were the same thickness, so it was a successful night. I'll probably show off a picture of the knife when it's finished. The scales are paper birch crotch from my home place, and these Hock kitchen knife kits make great gifts for the foodies in your life.
The tape isn't the thick foamy stuff you usually see, nor the wimpy office stuff. It's strong like carpet tape, but thin and incompressible like the office stuff - - best of both worlds. Buy it here, and tell 'em Jim sent you!