As per our Inbox Zero rule #3, you should automate the removal of unimportant emails from your Inbox to a separate folder that you can scan later. This can be easily done using EmailPet.
Since we don't want to create one rule per sender, we'll just create a list to store all the senders of unimportant emails.
Using your webmail interface or email client, create a new folder called Later.
Note that you'll need to click the "Refresh Email Folder List" option from the account drop-down menu on the top-right to update EmailPet's knowledge of this new folder.
Create a filter to add the sender of any email dropped into the Later folder to the Later address list.
Create a new filter to move all new email from senders in the Later list to the Later folder.
And that's it. As you move emails from your Inbox to your Later folder, EmailPet will learn the senders of such emails, and automatically move new emails from those senders into the Later folder.
This keeps your Inbox nice and tidy, and you can now read these unimportant emails at your leisure on occasion instead of being interrupted by them as they arrive.