ChordName/Staff Spacing

[Matthew Schulkind]

How can I squish ChordNames and Staffs closer together than they
willingly want to go?

I have tried:
\set Staff.minimumVerticalExtent = #'(0.2 . 0.2)
\override SeparatingGroupSpanner #'padding = #'0.2

and 

\set ChordNames.minimumVerticalExtent = #'(0.2 . 0.2)

Yet I still can't squish them as much as I want. There's still a
considerable amount of space surrounding the staff and names. How can
I get rid of even more?

Thanks,
Matt