Hi, I used to have old email being pushed twice, which is really annoying..
I used to use Delete Prior from my handset, but when I deleting my email manually, such problem never occurs to me again (it's been more than a month). Selecting all your email manually and deleting them is quite a task if you got hundreds of them, but it's better than having the old one pushed back into your device again
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It happens on my Gmail account, never on Yahoo.. so perhaps the problem lies with Gmail.