The beauty (or downfall, depending on your viewpoint) of BIS is that it only pushes emails to your device that appear in your email INBOX folder.
Originally Posted by chiefgary
By that, I mean any emails that are filtered into subfolders (like spam, or custom filters you have set up) will NOT be forwarded to your phone.
If you're like me and have work email sent to your via BIS OWA, then setting up custom filters in your Outlook will stop those filtered emails from being pushed to your device.
Hope this helps.
EDIT: You can set up filters on any email account. I was just using Outlook / OWA as an example.