The parameters of the unedf2 nuclear energy density functional (EDF) model were obtained in an optimization to experimental data consisting of nuclear binding energies, proton radii, odd-even mass staggering data, fission-isomer excitation energies, and single particle energies. In addition to parameter optimization, sensitivity analysis was done to obtain parameter uncertainties and correlations. The resulting unedf2 is an all-around EDF. However, the sensitivity analysis also demonstrated that the limits of current Skyrme-like EDFs have been reached and that novel approaches are called for.