Hi Paul,

> As far as I can see the number given to \tweak or \hspace is different for 
> different sizes (number of digits). I was hoping that putting the \mark 
> \default in the \tempo markup would take up as much space as it needed.

Here’s another solution.

\version "2.25.24"

\layout {
  \context {
    \Score
    rehearsalMarkFormatter = #format-mark-box-barnumbers
    \override RehearsalMark.self-alignment-X = #RIGHT
    \omit BarNumber
  }
}

\fixed c' {
  \mark \default
  \tempo \markup Allegro
  a1 b c
}

\fixed c' {
  \set Score.currentBarNumber = #125
  \mark \default
  \tempo \markup Allegro
  a1 b c
}

Cheers,
Kieren.
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