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 o
n 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 $3times 10^{-4}$. 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 $1.3 pm0.4times10^{-10},textrm{cm}^3/textrm{s}$ for low repumping intensity.
