booking specifc code

I did try a search for this info, but I kept getting timed out.
Can you book a specific fare code on-line? I know you can choose 'Lowest' or 'Flexible' but I haven't seen a way to get increased granularity in the fare classes.
Can you book a specific fare code on-line? I know you can choose 'Lowest' or 'Flexible' but I haven't seen a way to get increased granularity in the fare classes.