Search in Mac Mail is less than awesome.  Houdah provides a great way to filter email.

But, I can't tell what happens when I either delete a result or drag it to trash.

The message file is in the trash, but the mail header still exists in Mail client.  And when I click on the header it does find the email.

When I do delete a result in Houdah, though, it can not be found again, though--as noted--it still exists.

So, simple questions:
1. Is it possible to delete messages from the results pane in Houdah?
2. If not, is it possible to bring the results up in Mail to delete from within the email client?

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When I delete a result in Houdah, it disappears from the Houdah results (as you say).  But re-appears if I do another Houdah search.  And that is because it is still a Mail message.

I agree that it does not get moved to the Mail Trash folder - which is what you would expect to be the correct behaviour.  That is probably a feature request (not a bug) as it requires calls to the Mail app.  Pierre will have a view on that!

Your questions:
1. Seems it is not possible to delete messages (move to Mail Trash) in Houdah.  
2. Double click in Houdah results.  That open the message in Mail.  Click on Trash icon in the top bar of the message window.  That moves the message to the Mail Trash.

A new search in Houdah will still show the deleted messages - they still exist (for 30 days or whatever you set) as messages.  That behaviour is consistent with Mail app which shows messages in the Mail Trash when you search All.

I am pretty sure that all the above is because Houdah does a file/spotlight search which works because all messages are stored as files and are indexed by Spotlight.  But Houdah does not search in the Mail database (nor in any other application's database) which is where mail folder info is stored.  The Mail folder location is not part of the file metadata which is what is indexed by Spotlight and searched by Houdah.

It is rather contorted but you can exclude Mail Trash items by adding some location exclusions.  You will have to find the locations of your mail Trash folders and add them as exclusions.  For example this exclusion ensures that Houdah ignores mail on my Gmail Trash folder:
~/Library/Mail/V5/B7AECA56-4939-482A-AA51-1147B9D7D3EB/[Google Mail].mbox/Bin.mbox
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Apple Mail downloads mail messages and stores these as files. HoudahSpot can find these files. Apple Mail also keeps a catalog of messages. I.e. it knows how many messages are in your inbox, what the subjects are, etc. When you select a message it goes and opens the file to show you the full message.

I don't recommend you delete message files from underneath Apple Mail. As you noticed, Mail still knows about the message and actually expects the file to be there. What it does when the file is missing is hard to predict. It could at some later point re-download the message from the server. Basically undoing your effort to clean up.

When you double-click a Mail message in HoudahSpot, it opens in Mail. From there you can delete the message by pressing the Trash icon in the toolbar. This procedure requires at least 2 clicks per message.

You should be able to automate the procedure using Apple Script. Check the "Find PDF Files That Need OCR Processing" blog post for an example of an Automator script that installs as Service. This is then available from the context menu in HoudahSpot. You could try a simple script that opens the selected message one by one in Mail and asks Mail to delete the current message. You could also try to extract the Message-ID values from the files and ask Mail to delete messages with matching ids.
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You are so right.

What Apple Mail does is redownload from the server.  When deleting the file behind Apple Mail's back, it doesn't sync with the mail server so the message is still there.  What happens when the message is not there is you end up with a detached header that is stuck.  Rebuilding the inbox is the only solution for that.

I do like the search so much in HoudahSpot, but Apple Mail also uses Spotlight, just with a cluttered and less capable interface.

I could use AppleScript or something like Keyboard Maestro but then there are more dependencies and more fragility/complexity.

So, I've gone back to Mail with "smart folders" and a minimal message header display.

The search for ideal email management is never-ending.

Thanks for confirming that this was not an ideal way to handle moldy email.
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