Fitting as many lines as possible on a page

[Tim Yang]

I have a single staff music that spans two or three pages using font
size 15. If I use between-system-padding=#4 and
between-system-spacing=#4, it will use 3 pages with 12 lines for first
2 pages and a single line on 3rd page. if the numbers are both #3,
then it uses 2 pages.   But I notice there is a large space below each
page.  When I set annotate-spacing = ##t I can see "47.46 space left"
which is a large space.

Why does Lilypond left so large space unused and draws only 12 lines
while insisting on printing on 3rd page?  How can I stuff as many
lines as possible on each page, which seems more reasonable?