The extension of the roadmap of shorter wavelength extreme ultraviolet and soft x-ray sources is a topic of considerable interest. We have studied the optimized emission from high power and/or high brightness sources based on unresolved transition array (UTA) emission. The peak UTA wavelengths follow a quasi-Moseley’s law as λ=33.82×R∞−1(Z−20.86)−1.61 nm for the laser wavelength of 1064 nm (the critical density of 1 × 1021 cm−3) and λ=165.8×R∞−1(Z−12.44)−1.94 nm for the laser wavelength of 532 nm (the critical density of 4 × 1021 cm−3), respectively. The photon flux decreased with increasing atomic number. We also mapped the optimum electron temperatures and corresponding charge states required to produce strong soft x-ray UTA emission with a photon flux of the order of 1014 photons nm−1 sr−1. The present quasi-Moseley’s law is sufficient for identifying the optimum element for numerous applications, such as material ablation and ionization, nanolithography, and in vivo biological imaging.