Quote - Firefly looks outside of the current bucket to check for stuff which would influence the current bucket;  an example would be displacement materials.  So,  instead of just looking at the 8x8 bucket, Firefly actually checks a border of a few pixels around the bucket for these effects.  That means some duplication of effort.

That border is less significant if you're using a 32x32 pixel bucket.  Less duplication of effort -and less frequent fetching-  allows the faster render - if you have the RAM to support it.

If you are rendering something which uses displacement to replicate fur effects, you need a pretty large bucket. I had a horrible time rendering the sub-image at the upper left of http://www.renderosity.com/mod/gallery/index.php?image_id=2127981&user_id=445066&np&np because the boa kept being cut off due to the displacement extending beyond the bucket size. I eventually used a very large bucket size.