I think what you want is for the mini-window
to shrink to zero lines. The mini-window's minimal height is currently fixed at one line: it can't be made (permanently) taller or smaller than that.
Since I'm currently trying to understand the mini-window resize code anyway, here's a patch that does that. It's far from complete (in particular, mouseover on the mode line is broken) and in no way fit for inclusion, so do be careful if you decide to test it.
However, having tried it, it's really annoying! IMHO, it would be much better to have the mini-window in a separate frame and auto-raise that when it's needed, possibly obstructing the modeline.