How to write a pretty \not \varepsilon

How can I write a pretty \not\varepsilon? I want something like \notin, since I use \varepsilon as a relation symbol like \in.

Since \varepsilon has a smaller width than =, the alignment with \not is not perfect. \not is optimized for =. Package centernot helps to center the \not a little better:

\documentclass{article}
\usepackage{centernot}

\begin{document}
$a \not\mathrel{\varepsilon} b$
$a \centernot\varepsilon b$
\end{document}


You can just juggle with the spacing a bit I'm not sure it classifies as pretty though:

\documentclass{article}

\def\noteps{\mathrel{\!\not\mathrel{\,\varepsilon\!}\,}}

\begin{document}

$a \notin b \noteps c$
\end{document}


I'm nor sure if it is pretty, but...

\documentclass{article}

\begin{document}

\def\nwe{\mathrel{\not\mskip-\thinmuskip\varepsilon}}

$a \nwe A$

\end{document}