How do I increase my chances of finding a nametag?

With fishing in Minecraft, you now have a small chance of finding unusual items like leather, leather armour, enchanted rods and bows, enchanted books, and even saddles and nametags.

I have a rod that has "Luck of the Sea II", which increases my chances of finding "treasure", and decreases my chances of finding "junk". I'm attempting to find a nametag, but so far my attempts have been fairly futile.

What items are considered "treasure" and what is considered "junk", and is there any way of further increasing my chances of find treasure, or even specifically nametags?

Solution 1:

Junk is any of the following items:

Bowl, Fishing Rod (Highly Damaged), Leather, Leather Boots (Highly Damaged), Rotten Flesh, Stick, String, Water Bottle, Bone, Ink Sac & Tripwire Hook

Treasure is:

Bow, Enchanted Book, Fishing Rod, Nametag, Saddle, Lily Pad, Fishing Rod (Enchanted)

With an unenchanted Rod, your odds are: 85% Fish, 10% Junk, 5% Treasure. With Luck of the sea I, it goes to 86.5%, 7.5%, 6%. Luck of the Sea II: 88%, 5% 7%, and Luck of the Sea III: 89.5%, 2.5% 8%.

If you get treasure, your odds of getting a name tag are 16.7% (1/6), so with Luck of the Sea II you have odds of 1.2% of getting a Nametag each time.

The only way to increase this would be to get Luck of the Sea III, which increases the odds to a whopping 1.3%.