MySQL InnoDB: autoincrement non-primary key

Is it possible to auto-increment a non-primary key?

Table "book_comments"

book_id     medium_int
timestamp   medium_int
user_id     medium_int
vote_up     small_int
vote_down   small_int
comment     text
comment_id  medium_int

Primary key -> (book_id, timestamp, user_id)

There will be no other indexes on this table. However, I would like to make the comment_id column autoincrement so that I can easily create another table:

Table "book_comments_votes"

comment_id  (medium_int)
user_id     (medium_int)

Primary key -> (comment_id, user_id)

Users would be able to vote only once per book comment. This table enforces this rule by the primary key.

Question:

Is it possible to auto-increment a non-primary key - as in, auto-increment the comment_id column in table "book_comments"?

Alternatives, Discussion.

I would like to do this for simplicity as explained above. The alternatives are not promising.

• Make the commnet_id PK and enforce integrity through a unique index on book_id, timestamp, user_id. In this case, I would create an additional index.
• Keep the PK and replace the comment_id in the book_comments_votes with the entire PK. This would more than triple the size of the table.

Suggestions? Thoughts?