How do I make Endermen spawn more frequently?

I'm playing vanilla Minecraft, and am getting ready to head to the end. I need Eyes of Ender (and hence Ender Pearls), and in my main hunting grounds (a large desert area) as little as one Enderman may spawn per night. Is there any way to "promote" Enderman spawning so I can get pearls more quickly?

Endermen require a 3x1x1 space to spawn and a light level of 7 or less. The darker the place the more likely it is to spawn, the only way to decrease spawn rates it to light up/fill in areas.

Ways to increase Endermen spawning in particular include stopping spiders or slimes from spawning instead by filling in areas below level 40 in slime-spawning chunks. Also get rid of 1x2x2 areas for spiders to spawn. You will still get normal levels of the other tall mobs (skeleton, zombie, creeper), but they do not have any unique spawning requirements so nothing can be done.

Using a sword with a looting enchantment with give you more enderpearls per Enderman. And going to The End will mean only endermen can spawn.

Mobs spawn between 24 and 128 blocks (spherically) of you. The spawn wiki page has a very good image showing the ranges of how far mobs will spawn and despawn.

If you're standing in the middle of a 40 square desert, a good third of that is not spawnable due to your presence.

Also be aware of the spawning caps. Apparently there's a limit of 70-80 hostile mobs (many of which may be underground.

Try this: before night, go up into the sky to at least ~100 blocks above your desert. This should despawn the underground. As night falls, go back down to an altitude of ~20-25 blocks. This should keep the influence of your presence to a minimum on the ground level. If you see more than 50 enemies, either kill or despawn them to stay below cap.