# Properly sort index containing utf8 characters?

If my input file is utf8 encoded, how to I create an index where the entries are properly sorted?

Minimal example

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{makeidx}
\makeindex
\begin{document}
Hello World\index{Gödel}\index{Galois}
\printindex
\end{document}

After compiling with pdflatex and makeindex, the entries show up with “Gödel” before “Galois”, which is wrong.

In another somewhat related question it is suggested to compile with xelatex instead; however I'm trying to do this in a large-ish project already written by someone else, and trying to switch to xelatex is proving a bit problematic.

So, is there a way to make it work with pdflatex?

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