SMS Notification Taskbar Icon Only No Popup

[firefurby]

I know how to get rid of it all together. That's simple enough. The question I have is much trickier and I've tried searching for an answer, but keeping finding ways to just turn it out completely.

When I was first trying to get rid of the notification I came across a post where someone had found a way to get rid of the Pop-Up, but still have the icon in the Taskbar show up. Does anyone know how to recreate this behavior? TIA