If I use mathpazo then it seems that \left\Vert and \right\Vert generate the wrong size in one case:
\documentclass[11pt]{article}
\usepackage{mathpazo}
\begin{document}
{\Large $\left\Vert X_f\right\Vert$}
{\large $\left\Vert X_f\right\Vert$}
{\normalsize $\left\Vert X_f\right\Vert$}
{\small $\left\Vert X_f\right\Vert$}
{\footnotesize $\left\Vert X_f\right\Vert$}
{\scriptsize $\left\Vert X_f\right\Vert$}
{\tiny $\left\Vert X_f\right\Vert$}
\end{document}
Notice how the fourth \Vert is the wrong size:

Is this a bug or a feature? And how to I get rid of it? Saying "do not use \left and \right" is not a valid answer until you also suggest how I might get the following macro working without them:
\newcommand{\trunc}[2]{\mathopen{}\left\Vert #2\right\Vert_{#1}\mathclose{}}
It has to be one macro, the book is already written using it. As far as I am concerned this is not my fault, but that of mathpazo.

\leftand\right, they produce an extra horizontal space and they quite often produce too large delimiters. – yo' Jun 10 '13 at 22:13\Vertdepending on the size of the argument. Let me amend the question. – Andrej Bauer Jun 10 '13 at 22:18\Vert-- it applies to all other delimiters too, at least all the ones I've tried. – Mike Shulman Jun 10 '13 at 23:11\smash[b]on only the subscript (requiresamsmath) would be an improvement, but it may not be practical. i'll take a closer look, with other delimiters as well as\Vertand parentheses (as in your original formulation). – barbara beeton Jun 10 '13 at 23:18\delimitershortfall=10ptand\delimiterfactor=750. This is not just a problem withmathpazo, try compiling with\usepackage{mathpazo}removed. Then the scriptsize and tiny delimeters are poorly sized. Compiling the document at 10,11 and 12pt produces surprising results, withmathpazoand also withoutmathpazo. – corporal Jun 11 '13 at 01:16fsubscript - replacing it withgdoes not display such drastic behaviour. – Andrew Swann Jun 11 '13 at 07:57\delimiterfactorand\delimitershortfallfix it? Personally, I would really like to understand, not just slap on a quick fix that acts like magic to me. – Mike Shulman Jun 11 '13 at 14:43