>> BTW I do not understand well in which sense your original scenario
 >>
 >>    (pop-to-buffer (generate-new-buffer "*edit string*")
 >>                   '(display-buffer-below-selected
 >>                     (window-min-height . 10)
 >>                     (window-height . fit-window-to-buffer)))
 >>
 >> fails.  Do you mean that the window should be at least ten lines high
 >> despite of the fact that it's fit to an empty buffer?
 >
 > Exactly.  I expected that window-min-height takes precedence over window-height.

We could do something like the untested attached .diff.  But we really
should install it only if at least two or three people confirm that it's
the expected behavior.

Note: ‘shrink-window-if-larger-than-buffer’ does not re-enlarge a window
that already shows the buffer if its height is less than the specified
'window-min-height'.

martin