There has been a few mentions of "pulling on the handlebars". Unless you're sprinting, or really attacking, you shouldn't need to do that. Go to about 1:50 in that video and watch Contador in his high-cadence climbing pace. You can see how relaxed his grip is on the bars, and he's pushing down as much as he's pulling up. If you feel the need to pull up on the handlebars to off-set your down pressure on the pedals, that means you're not using your rear leg effectively enough.

It may seem counter-intuitive, but I often climb out of the saddle (on longer climbs) to give my quads a break. Really concentrating on pulling my rear leg up from the hip, using the psoas and glutes, then engaging the hamstrings in the top half of the pull, allows me to do nothing but stand on my front leg (no extra push necessary). Doing this for 10 or 15 revolutions can give the quads a little reprieve while the load gets distributed elsewhere, so that they're more fresh when I sit back in the saddle to continue grinding away.

The fastest way up a climb is to use every muscle group on ever revolution. But that's also the fastest way to overcook.

You'll know you're doing it right when you can rest your hands on top of the bars with only a light grip (for side-to-side stability), and you aren't bobbing up and down all over the place.