The H gamma and H delta absorption features are measured in a sample of 455 (out of an original 460) Lick/IDS stars with pseudo-equivalent width indices. For each Palmer feature, two definitions, involving a narrow (similar to 20 Angstrom) and a wide (similar to 40 Angstrom) central bandpass, are measured. These four new Balmer indices augment 21 indices previously determined by Worthey et al., and polynomial fitting functions that give index strengths as a function of stellar temperature, gravity, and [Fe/H] are provided. The new indices are folded into models for the integrated light of stellar populations, and predictions are given for single-burst stellar populations of a variety of ages and metallicities. Contrary to our initial hopes, the indices cannot break a degeneracy between burst age and burst strength in post-starburst objects, but they are successful mean-age indicators when used with sensitive metallicity indicators. An appendix gives data, advice, and examples of how to transform new spectra to the 25-index Lick/IDS system.