Inertial confinement fusion (ICF) cryogenic experiments on the 60-beam OMEGA laser have strict requirements for the laser energy delivered on target to be power balanced in order to maximize target-irradiation uniformity. For OMEGA, this quantity (power balance) is inferred from measurements of the time-integrated energy and time-resolved, spatially integrated temporal profile of each of the 60 beams at the output of the laser. The work presented here proposes a general definition of power balance as measured at the laser output and discusses the conditions that are fundamental to achieving laser power balance. Power balance necessitates equal gain across all stages of amplification, equal net losses across each amplifier stage, equal frequency conversion (from 1053 nm to 351 nm) of all 60 beams, and equal beam path lengths (beam timing). Typical OMEGA ICF laser pulse shapes consist of one or more short (100-ps) "pickets" followed by a shaped "drive" pulse of 1 to 2 ns. For these experiments, power balance is assessed for the pickets and the drive independently, with the ultimate goal of achieving root-mean-square (rms) imbalance across all 60 beams of less than 2% rms on both. This work presents a comprehensive summary of laser shot campaigns conducted to significantly improve laser power balance from typical rms values of 4.7% and 5.2%, respectively, to the 3% level for both features along with a discussion of future work required to further reduce the rms power imbalance of the laser system.