One of the most important things to do in Minecraft is mine, and in Middle Earth, it is still pretty important.  This is the mining strategies that work for me.

Step 1: Where to mine.

There are many biomes in this mod, and many have advanteges and disadvantages for miners.  Because I have never played as evil, this will mostly be targeted toward good players.  For one thing, some biomes, for example, Shire, Lothlorien, Lindon, and Blue Mountains, do not spawn enemys.  This means you can explore caves in peace.  You may consider these biomes if you are not too good at fighting.

Even more importantly however, is the fact that some ores can only be found in certain biomes.  Mithril is only in the Misty Mountains, Quendite is only in Lothlorien and Lindon, and glowstone is only in the Iron Hills and Blue Mountains.  Also, the Red Mountains have twice as much ore as everywhere else.  You will probably end up mining in more than one biome to get the ores you want.

Step 2: Mine

After you have picked much biome to mine in, you will need to start mining.  This is a mining method that works well for me.  Get a whole buch of ladders and a bucket of water.  Dig a hole 1 X 3 down to the level you want to mine at.  I like y=12.  On one side of the hole, dig two down and pour the water.  On the other side, place the ladders.  I then pillar jump up the middle with the cobblestone I just got, but I don't think it is neccessary.  Whenever you want to mine, you can just jump down on the side with the water, and use the ladders to get back up.  Once I am at level 12, I mine using the feather method.  Pretty much you have a 1 X 2 tunnel with 1 X 2 tunnels branching off a regular intervals of 4 or 5 blocks.  Lastly, remember not to dig straight down!

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