I have started using gmail thru Thunderbird and every incoming email is duplicated 3 times (it will appear once in the 'Inbox' folder, once in the 'Gmail/All Mail' folder and once in the 'Gmail/Important' folder).

This is annoying because I have to open the same email 3 (once every copy of it) times to ensure that the notification icon doesn't signal three unread mails. So I have to always go to the 'Gmail/All Mail' and 'Gmail/Important' folders to mark folder as read every-time I get a new mail.
How can I remove the 'Gmail/All Mail' and 'Gmail/Important' folders in Thunderbird (obviously without deleting the content of 'Inbox')? Is this something that can be fixed from within Thunderbird, or do I have to change something on the webmail side?