Avoid parskip overstretching

Question

What I want to archieve:

Layout where \raggedbottom is in effect and parskip stretches the paragraphs as far as it is configured to do. Like so:

\raggedbottom
\setlength{\parskip}{11pt plus 5pt minus 5pt}

I would expect that parskip would stretch out the paragraphs up to 5pt (or shrink thema by 5pt), but what happens is: nothing.

If I use \flushbottom the paragraphs are stretched to fit the page no matter what I use. The only difference is the report of badness depending on if parskip is overstretching or not.

So my question would be: Is there a way to archieve the desired result of parskip stretching to the given values but not more regardless if \flushbottom is archieved or not?

Edit per request:

No stretching at all:

\documentclass{article}
\addtolength\textheight{-10.7\baselineskip}
\setlength{\parskip}{0pt plus 11pt}
%\flushbottom
\begin{document}
   aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa
bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb
\pagebreak
ccc
\end{document}

Stretched to the max (far more than "allowed" by parskip):

\documentclass{article}
\addtolength\textheight{-10.7\baselineskip}
\setlength{\parskip}{0pt plus 11pt}
\flushbottom
\begin{document}
aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa
bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb
\pagebreak
ccc
\end{document}

I would like it to be somewhat in the middle: stretch as far as parskip allows but not further.

(Example shamelessly borrowed from How do parskip and similar parameters behave)

Answer 1

by default \raggedbottom adds

plus.0001fil

glue to the bottom of the page, this is infinite order so no finite order glue will stretch so your \parskip is effectively 0pt.

So you can redefine \@textbottom to use finite glue (eg 0pt plus \textheight) or define \parskip to have fil glue (which would allow it to grow without limit without accumulating badness)

So probably you want

\def\@textbottom{\vskip \z@ \@plus \textheight}

so the stretch is distributed between the bottom of the page and between paragraphs.

Note however that if glue stretches you can not give it an upper bound

\setlength{\parskip}{0pt plus 11pt}

Does not mean that the glue may stretch to at most 11pt, the plus value is used in the badness calculation, so as the glue expands beyond that the badness of the page increases rapidly, but it will still stretch beyond that if that is needed.

All finite glue will stretch by the same factor so the end of page space will stretch more than the inter-paragraph space by the same ratio as \textwidth to 11pt.

---

If there is only one paragraph break and textbottom has full textheight stretch the parskip stretches a bit but is just noticable

If you only give .4\textheight at the bottom, you get more stretch in parskip

If you only allow .1 textheight, then parskip stretches more but now there is not enough stretch to fill the page without an underfull box warning

Underfull \vbox (badness 1253) has occurred while \output is active

\documentclass{article}
\addtolength\textheight{-10.7\baselineskip}
\setlength{\parskip}{0pt plus 11pt}
%\flushbottom
\makeatletter
\def\@textbottom{\vskip \z@ \@plus .1\textheight}
\makeatother
\begin{document}
   aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa\\aaaa
bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb\bbb
\pagebreak
ccc
\end{document}