Leadsheet - trying to fill page without leaving empty space

[Michael Hendry]

Oh Wise Ones,

I use Lilypond to produce jazz leadsheets for concert, Bb and Eb instruments, 
and find I often have to tweak parts to get them to fit on to a single A4 page.

Alto sax parts tend to need a bit more compression because they tend to have 
more ledger lines at the top of the staff.

I can usually get a reasonable result by tweaking global-staff-size, but here’s 
an example of the bottom of a page with 

#(set-global-staff-size 14.75)

https://www.dropbox.com/s/l1c8rggolebqox0/Screenshot%202019-06-10%2016.52.02.png?dl=0

and here’s the same song with

#(set-global-staff-size 14.76)

https://www.dropbox.com/s/q5vcp4ktf4wgb7m/Screenshot%202019-06-10%2016.52.48.png?dl=0

Although there’s a substantial gap between the last bar of the former and the 
footer, the latter forces the last three bars to a second page.

Am I tweaking the wrong parameter?

Is there a more elegant way of ensuring that a leadsheet fits in one page?

Regards,

Michael