The purpose of the QOMA II project (funded by the European Space Agency-ESA) is to implement a Diode Pumped Solid State-DPSS laser with pulses of energy >10 mJ and duration <15 ns (100 Hz repetition frequency and M2<1.2). To this end, pumping of multisegmented Nd:YAG rods directly to the upper laser state (885 nm) will be used, together with conductively crystal cooling in passively Q-switched mode. Our simulation results showed that energies >10 mJ/pulse and M2<1.2 are achievable.