Now that Kicksome's shamans and I have cleared the 1700 mark, we're starting to see more and more of these two compositions.

Not speaking from much experience on beating them consistently, I only have theories on the best way to handle them.

Anyone have any experience in consistently beating these two comps?
What is the preferable targeting order for these two comps?

"Triple Healer" aka "Cleave"
(The comps I've gone up against have two MS warriors, and three healers, i.e., resto druid, holy pally and resto shaman or priest.)

I've come to the conclusion that you have to start a healer, preferably the druid to prevent cycloning, and then switch to one of the two warriors. Or maybe we need to target one healer - throw a volley, switch to another healer and throw a volley before switching a warrior and triggering NS. I'm not sure which strategy would be better.

Last night, when we faced this composition, we targeted one warrior from the outset, and switched to the other, but I'm convinced they knew exactly what we were going to do, because
A) it makes the most sense for us to get down a DPS quick and
B) if we're targeting warrior then because we're a 4 DPS team, we must be going for warrior B.

From what I can tell, they had one healer dedicated to one warrior, one healer dedicated to the other warrior (spamming), and the druid dedicated to keeping me (holy pally) out of the fight).

"Triple Melee"
(The comps I've seen have three physical dps: Enhancement Shaman (ouch!), MS Warrior and Rogue or Ret Pally, and two healers: holy pally and disc priest.)

We don't have as difficult of a time with this team makeup as the triple healer but it still gives us problems due to the enormous damage output.
Does anyone ever try to take a healer down first? I would imagine that would be the last thing they would expect.

Right now, we try to get one of the DPS down first, really any of them if the right opportunity strikes, and then work on a healer or another DPS depending on the circumstances, but our strat has to be a lot more fluid than with a triple healer.