Mail doesn't put deleted messages into trash.

I've got two IMAP accounts that are set up slightly differently.

One one (call it account P), my mailboxes show up in a drill-down list
under that account's inbox. On the other (account M), my mailboxes show
up at the same level as my inbox for that account. I'm sure this has to
do with the namespace the two providers used to set up the mailboxes.

The problem is that on account P, messages I delete from my inbox are
lost forever. They don't end up in my trash. Deleted messages from
account M do end up the trash. Under my Trash icon, I've got two
mailboxes, one called "On My Mac", the other called M.

In the Preferences/Accounts tab for both accounts, I've got both "Move
deleted messages to the Trash mailbox" and "Store deleted messages on
the server" checked.

Anybody have any idea what might be going on? Is there some additional
logging I can turn on in Mail to make it show more details of what it's
doing?