Are there any reasons to not use smallint when it fits the data?

Since PostgreSQL doesn't have 1-byte tinyint, the second best option would be smallint. However, I've read from various posts* that it may actually be slower because CPU's are optimized to operate on 32-bit integers, or there may be implicit conversions to 32-bit integers. Besides these reasons, are there any other reasons I'm not yet aware of for not using integers smaller than 32-bits? \* I can't find it now, and I could be wrong about this. What I understood from it is that smaller integers would save disk/index space. So, good for the database, but the web/computation server would need to convert it to 32-bit