to more than ten magnitudes of absorption in the $uvm2$ and $uvw2$ filters. Hence, from now on, we will only consider the $A_{\rm V}~\leq~4$ domain. The mean $E(uvw2-uvw1)/E(u-uvw1)$ colour excess ratio over this range is $-2.83$ ($\pm\,0.27$). It is worth to note that $(uvw2-uvw1)$ and $(u-uvw1)$ are, with $(u-b)$ and $(b-v)$, the only pairs of colour indices allowing the definition of a reddening free index over a reasonable range of stellar parameters.

In order to define the reddening dependent index, that we will call $ic_{\rm red}$, the most obvious choice is the empirical $$ic_{\rm red}~=~uvm2~-~(uvw1~+~uvw2)\,/\,2.$$ This index could be used but it is not really independent from $ic_{\rm 0}$ and its reddening dependence can be ameliorated. Indeed, though the $uvm2$ filter stands on the $2175$ Å absorption bump, the $uvw1$ and $uvw2$ filters are not symmetric with respect to it, and of more importance, the $uvw2$ filter is significantly affected by the $2175$ Å absorption bump too. To refine the choice, we explored a large number of UV magnitude combinations and were finally brought to the conclusion that the best choice in terms of simplicity and dynamics of the index (and hence in terms of accuracy) is $$ic_{\rm red}~=~uvm2~-~uvw1$$

There 