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Thanks for your responses. I should have been more clear. But then, I did write: "[Followed by a chapter's worth of additional text.]" :)

I was trying to get the code down to its bare essentials to see if anyone else could replicate the problem.

So yes, you do need a bunch of text for \flushbottom ...

Esteemed TeXperts:

\flushbottom (and thus vertical justification) doesn't seem to be working with the Memoir class (either in MikTeX or TeXLive). I've narrowed my test document down to this:
\documentclass{memoir}
\widowpenalty=10000
\flushbottom
\begin{document}
\chapter{Captain Rogers}
A man ...

Esteemed TeXperts:

If I process a LaTeX file (using pdflatex) in MikTeX 2.4, vertical justification works fine. In other words, space between lines of text is stretched or compressed to avoid widows. Here's the kind of thing I'm doing (with extraneous stuff removed for clarity ...