  We report an experimental study of peak and phase-space density of a
two-stage magneto-optical trap (MOT) of 6-Li atoms, which exploits the narrower
$2S_{1/2}\rightarrow 3P_{3/2}$ ultra-violet (UV) transition at 323 nm following
trapping and cooling on the more common D2 transition at 671 nm. The UV MOT is
loaded from a red MOT and is compressed to give a high phase-space density up
to $3\times 10^{-4}$. Temperatures as low as 33 $\mu$K are achieved on the UV
transition. We study the density limiting factors and in particular find a
value for the light-assisted collisional loss coefficient of $1.3
\pm0.4\times10^{-10}\,\textrm{cm}^3/\textrm{s}$ for low repumping intensity.
