This paper models recent experiments in which a solid titanium target was illuminated by several joules of combined energy from a nsec laser pulse to create a preplasma followed by a psec laser pulse to drive the gain. Gains greater than 200 cm-1 are predicted for the Ne-like Ti 3p 1S0 yields 3s 1P1 transition at 32.6 nm which is driven by the monopole collisional excitation. High gain is also predicted for the 3d 1P1 yields 3p 1P1 transition at 30.1 nm which is driven by a combination of collisional excitation and self photopumping. We also discuss the possibilities for driving a Ne-like Ge laser using this approach. For the Ni-like ions we model a solid molybdenum target under similar conditions used for Ti and predict gains greater than 300 cm-1 for the Ni-like Mo 4d 1S0 yields 4p 1P1 transition at 18.9 nm which is driven by the monopole collisional excitation. High gain is also predicted for a self photopumped 4f 1P1 yields 4d 1P1 transition at 22.0 nm and several other transitions driven by inner shell collisional ionization.