Lifting large nails from hardwood joists

I recently lifted some rotted decking and was left with a bunch of largish nails protruding from the hardwood joists. I tried to lift them out with a claw hammer but they were firmly rooted in the joists and refused to budge. I purchased a Easwing wrecking bar in the foolish belief that such a fine instrument would hook under the head of the nails, but its claw is all but useless, not gripping either the shaft or the head. There are the Japanese nail lifters at Carb-Tech but from the web site they look like they might be too small to pry nails of that size. I'm guessing the nails are about 3mm with round heads and protrude about 20-25mm. Any ideas?