Make a 16x16x3 room at bedrock, then two more above it. Then just go do other stuff and come back later. It should be bursting with slimes.

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Do as Burnmad said, but you can keep going up until you reach layer 40. Last I heard that is the top layer a slime can spawn on.

No, not on the 360 Edition yet. They only go up to 12 (Or was it 16?) right now, I think.

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If you want to maximize slime spawning, light up EVERYTHING. Seriously, in a big radius around the target point, you need to make every nook and cranny to bright for baddies to spawn. Then you'll be swimming in slimeballs (eww...).

Ew? That sounds awesome!

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Got slimes; I just had to wait a bit longer, lol.

Took me forever to figure out the door I was building, though... Most complex thing I've done with redstone is a 2-note doorbell, and even that was a pain. Plus, all the tutorials online are for 2x2 Jeb doors and not the 3x2 simple sliding one I was building, so I kinda had to figure that out on my own.

Achievement Hunter has a thing for those, but theirs was powered by pressure plates, and I wanted levers on both sides, so I had to figure out just what I needed to do in the first place. It was a lot simpler than I thought it would be, once I figured out what xor gates and inverters are.