I had two gmail accounts. I created a new account with a pretty popular privacy respecting mail provider. I wanted the first gmail address as a backup (if the privacy respecting one does not work on some sites) while completely deleting the second gmail account.

I wanted some emails from both of these accounts to the new mail provider. So I exported from the first gmail account and then mass deleted all other unimportant mail from the first gmail account.

Then, I did opposite for the second gmail account. I first mass deleted from the second gmail account but then got locked out from my own gmail due to 'suspicious activity'. So now, I can neither import some mails from my second gmail account and neither can delete the entire account, the way I wanted to do it.

Luckily, the second gmail account was the useless one. I tried to unlock it to get my mails, but as usual there is no one to contact at google.