I'm new, so go easy on me, but I'm aware of alternate picking, for a single string. Is there a technique similar to alternate picking that applies to all three strings (D A D) to increase the speed of your drop D power chords?

try doing hammer ons and pull offs with drop d chords if you want a boost in technique.

i know of one example though...

tool - aenima.

might be difficult but imo it's easy as...

Just downstroke and upstroke, like alternate picking, but hit the D A D strings instead of just one. It may feel a bit awkward at first, but the more you practice it, the faster you'll get.
Quote by DevilsDance76
rigeljs is on the money...

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The advantage of drop d is that you can hammer on and slide power chords easily, often without needing to strum. Use that to your advantage.