The goal of the present study is twofold. First, we employ new HST/STIS spectra and photoionization modeling techniques to determine the progenitor masses of eight planetary nebulae (IC 2165, IC 3568, NGC 2440, NGC 3242, NGC 5315, NGC 5882, NGC 7662, and PB 6). Second, for the first time we are able to compare each object’s observed nebular abundances of helium, carbon, and nitrogen with abundance predictions of these same elements by a stellar model that is consistent with each object’s progenitor mass. Important results include the following: (1) the mass range of our objects’ central stars matches well with the mass distribution of other central stars of planetary nebulae and white dwarfs; (2) He/H is above solar in all of our objects, in most cases likely due to the predicted effects of first dredge-up; (3) most of our objects show negligible C enrichment, probably because their low masses preclude third dredge-up; (4) C/O versus O/H for our objects appears to be inversely correlated, which is perhaps consistent with the conclusion of theorists that the extent of atmospheric carbon enrichment from first dredge-up is sensitive to a parameter whose value increases as metallicity declines; (5) stellar model predictions of nebular C and N enrichment are consistent with observed abundances for progenitor star masses ≤1.5 M⊙. Finally, we present the first published photoionization models of NGC 5315 and NGC 5882. Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555.