How to Disable Popup Preview of Messages?

Hi. I'm just trying to figure out if there's a way to stop Mail.app from popping up the small preview of messages in the top right corner of the screen when they're first received. I find this incredibly annoying. I've searched thoroughly for a solution to this, but all I can find is how to remove the preview pane, which is not what I need to do. I don't know anything else to call this feature besides a "preview," which makes it hard to search for a solution, since so many of the results center around the preview pane. I would greatly appreciate any help you can offer. Thanks.