This report describes that the enchanting table does not show three enchantments for fishing rods if too few bookshelves are placed around it.
See MC-36937 for the bug that a first enchantment is shown despite it not being available.
You cannot enchant fishing rods with enchantment levels < 4, as clicking the available does nothing. Tested in survival and creative
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Still have the issue, i cannot put level 1-4 enchants on fishing rods. The enchantmens were showing fine when i put level 5 or higher on rods. See my attached file. When i click the level 1 row, nothing happens (the rod is NOT enchanted and i keep my level). Tools etc. work fine
Edit: I am on Linux, but I guess this makes no difference

Confirmed.
Still in 13w37a. Level 4 enchants seem to work, my bad. Level 1-3 still dont do anything
Confirmed on SMP in 13w37b.
Still present in 13w38c (single player, survival)

Still in 13w39b
Confirmed in SSP 13w41b.

If you can't enchant with a level, it simply has no enchantments available for that cost.
I thought it was too easy...
I still experience this in the new 1.9 release

@unknown: Most probably you're experiencing MC-36937
@Kumasasa: I agree

I’ve reviewed the two tickets and they’re set up properly. This is not a duplicate of MC-36937.
Cannot confirm with 13w36b. Are you sure you're not on 13w36a ? See MC-29462