Accounts with those providers (and gmail) automatically copy sent messages to Sent, so you should uncheck 'Place a copy in' in the Copies & Folders section of Account Settings for each account.

Beautiful. Thank you!

Double outgoing messages is my problem, too.

I found the Copies & Folders section, but could not open it: "This account exists already. Give it a new name."

"Copies & Folders" was in duplicate as were all other account settings and folders.

How do I remove the duplicate?

Olliko said

Double outgoing messages is my problem, too. I found the Copies & Folders section, but could not open it: "This account exists already. Give it a new name." "Copies & Folders" was in duplicate as were all other account settings and folders. How do I remove the duplicate?

The Account Name is at the top when you open Tools/Account Settings and select the account in the left pane. It usually defaults to the email address, but you can change it so it's different from the Account Name for another account.

I found out in the settings that there was a duplicate account in duplicate the settings (why, I have no idea). The problem was solved, when I removed the duplicate account.