Measures of the depletion of interstellar elements from the gas phase are usually derived by assuming that the general composition of the interstellar medium is identical to that of the Sun. A compilation of stellar composition data, including B stars as well as field F and G stars, however, calls this assumption into question. In this Letter we consider the impact on derived depletions if the reference abundances are derived from stars in the solar neighborhood rather than from the Sun, and we discuss the implications for current models of the interstellar dust. Using recent, accurate gas-phase column densities for zeta Ophiuchi, we show that the systematically lower depletions resulting from our revised cosmic abundances are in conflict with most dust models because insufficient quantities of raw materials are available to explain the observed extinction. A Kramers-Kronig analysis for the zeta Oph line of sight shows that the revised depletions are consistent with the required opacity of interstellar dust only if the density of the grain material is near 1 g cm-3, suggesting that the grain structure must be open (i.e., the grains must by fluffy, porous, or fractal in structure).