Re: Apple mail - delete versus trash :
I find it annoying that when I "delete" mail, it doesn't go away, but gets thrown in the trash,
Seems you haven't (yet surely many of us have) thankfully recovered a deleted email from the Trash!
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Re: "I have to delete it again to make it go away".
We often have the choice in Mail settings for how long deleted emails remain in the Trash (or Archive)
Delete and recover emails in Mail on iPhone - Apple Support
Eg: says:
"Decide how long to keep deleted emails
With some email clients, you can set how long deleted messages stay in the Trash mailbox.
- Go to Settings
> Apps > Mail. - Tap Mail Accounts, then do one of the following:
- If you’re using an iCloud email account: Tap iCloud, then tap Mailbox Behaviors.
- If you’re using another email account: Tap an email account, tap Account Settings, then tap Advanced.
3.Tap Remove, then select a time interval.
Note: Some email services might override your selection; for example, iCloud doesn’t keep deleted messages longer than 30 days, even if you select Never."
Eg: My Yahoo Trash has a choice of "Never" / "After one day" / "After one week" / "After one month"
(NB: however GMail doesn't seem to have that choice in "Advanced" settings)
(NB: The linked article above also has other interesting tips too)
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Re: "How can I do one-step deletion of mail?"
Once mail is deleted (and in the trash), it is automatically deleted after the time chosen in settings
I don't know any way of achieving "instantaneous deletion" in one-step though. May be rather risky.