  We present the first results from applying the spectral inversion technique
in the cloudy L dwarf regime. Our new framework provides a flexible approach to
modelling cloud opacity which can be built incrementally as the data requires,
and improves upon previous retrieval experiments in the brown dwarf regime by
allowing for scattering in two stream radiative transfer. Our first application
of the tool to two mid-L dwarfs is able to reproduce their near-infrared
spectra far more closely than grid models. Our retrieved thermal, chemical, and
cloud profiles allow us to estimate $T_{\rm eff} = 1796^{+23}_{-25}$ K and
$\log g = 5.21^{+0.05}_{-0.08}$ for 2MASS J05002100+0330501 and for 2MASSW
J2224438-015852 we find $T_{\rm eff} = 1723^{+18}_{-19}$ K and $\log g =
5.31^{+0.04}_{-0.08}$, in close agreement with previous empirical estimates.
Our best model for both objects includes an optically thick cloud deck which
passes $\tau_{cloud} \geq 1$ (looking down) at a pressure of around 5 bar. The
temperature at this pressure is too high for silicate species to condense, and
we argue that corundum and/or iron clouds are responsible for this cloud
opacity. Our retrieved profiles are cooler at depth, and warmer at altitude
than the forward grid models that we compare, and we argue that some form of
heating mechanism may be at work in the upper atmospheres of these L dwarfs. We
also identify anomalously high CO abundance in both targets, which does not
correlate with the warmth of our upper atmospheres or our choice of cloud
model, and find similarly anomalous alkali abundance for one of our targets.
These anomalies may reflect unrecognised shortcomings in our retrieval model,
or inaccuracies in our gas phase opacities.
