There's a software solution for this. The most secure way is on your own computer. Using IMAP to download those directly from your provider so you can then delete them.
Webmail Archive Manager does just this. Downloads all emails in any folder(s) that you select. It has the entire email (text, rendered/code html, attachments, all the recipients, all the CCd and the full header for forensics). You can search, reorganize, whatever you like.
I'm not sure what the policy is on links but it's here:
http://maxedge.com/
If that link doesn't show up, just google Webmail Archive Manager....it's by MaxEdge. Oh...it's cheap too.
-MichaelMac