# superscripts on customized unit in siunitx

I want to add subscripts to some units and so far the solution I found is to define my own unit, for instance:

 \DeclareSIUnit{\Lmedia}{\text{$\textup{L}_{\textup{media}}$}}


However, when I use this with \SI the superscript is too far away. Here's a MWE of what I mean:

\documentclass{article}

\usepackage{siunitx}

\DeclareSIUnit{\Lmedia}{%
\text{$\textup{L}_{\textup{media}}$}%
}

\begin{document}

\SI{1}{\mol\per\milli\Lmedia}

\end{document}


How can I fix this? or alternatively, is there a better way to include my own subscripts?

\documentclass{article}