Keyboard Shortcut - Floating Window Docking?

Hi everybody,

I like the ability to dock windows sometimes, but I don't like the frame hotspot that auto-docks my windows if it gets to close. I'm often shrinking windows to thumbnail size and putting them in the corner to retrieve/compile, but don't want the nagging border that keeps wanting to dock them.

Instead, is there a shortcut that upon pressing it docks the window in focus? Just being able to dock things that way would be really nice.