The high efficiency method of transient collisional excitation has been successfully demonstrated for Ne-like and Ni-like ion x-ray laser schemes with small 5-10 J laser facilities. Our recent studies using the tabletop COMET (Compact Multipulse Terawatt) laser system at the Lawrence Livermore National Laboratory (LLNL) have produced several x-ray lasers operating in the saturation regime. Output energy of 10-15 {micro}J corresponding to a gL product of 18 has been achieved on the Ni-like Pd 4d {yields} 4p transition at 147 {angstrom} with a total energy of 5-7 J in a 600 ps pulse followed by a 1.2 ps pulse. Analysis of the laser beam angular profile indicates that refraction plays an important role in the amplification and propagation process in the plasma column. We report further improvement in the extraction efficiency by varying a number of laser driver parameters. In particular, the duration of the second short pulse producing the inversion has an observed effect on the x-ray laser output.