Better Search Bar for Sidebar

[RayZ3R0]

Im suggesting an enhancement for a better searchbar on the right/left toolbar. Currently its like this

Would it be possible to make it so the text box is very small, and does not overflow when the sidebar is not expanded, but when its clicked, it will be slightly popped out, and minimized if its out of focus again.

Also, would it be possible to make the search bar show suggestions and autocomplete links? Would be nice if everything was inside sidebar so no horizontal panel.