Low noise CW milliWatt scale UV lasers are needed for many analysis applications in the semiconductor and the biological fields. Intracavity tripling has been widely used to improve the UV output power of Q-switched or modelocked lasers, but no efficient diode-pumped CW UV laser was ever reported. One of the key to success is the use of a monolithic laser structure which both eliminates the birefringence interference issue and facilitates the single frequency operation. The monolithic structure is obtained by optically contacting crystals. It does not require any alignment, reduces the manufacturing cost and improves reliability. The optimization of the amplifying medium and doubling and tripling crystals involves as many parameters as pump absorption, thermal lens, cavity length, 1064 nm mode size, walk-off, acceptance angles, polarizations, phases... The interplay between these parameters will be discussed. Finally, several amplifying media (Nd:YAG and Nd:YVO4), doubling crystals (KTP, KNbO3, BBO, BiBO and LBO) and tripling crystals (BBO, BiBO, LBO) were tested. With a 2.4W 808 nm diode pump, several configurations have led to low noise 355 nm single frequency operation exceeding 5 mW. We believe that this power can still be improved.