The reference abundance of the interstellar medium (the abundances of heavy elements in both the grains and the gas) is perhaps as low as 65% of solar, rather than solar as has been widely assumed in the past. Furthermore, ≍38% of the solar C/H is now known to be in the gas rather than in grains. The evidence for these statements is reviewed. These reductions in the amounts of heavy elements available for grains have profound significance for the nature of interstellar dust.Models to fit the new and much tighter abundance constraints are presented. They consist of small graphite particles (to produce the 217.5 nm bump), some small silicate particles, and composite grains containing carbon (either amorphous, hydrogenated amorphous, or graphitic), silicates, oxides, and possibly vacuum. Only the nature and size distribution of the larger grains (a > 0.05 μm) are constrained by the reference abundance because these grains contain most of the mass. This paper assumes that in the ISM all elements other than H and He are reduced by a factor ZISM/Zsun. The minimum values of ZISM/Zsun are achieved with one form of amorphous carbon (AMC). It can fit the usually accepted value of the extinction per H atom with a C/H = 155 x 10-6 (ppM) in the grains, including those producing the 217.5 nm feature. This abundance is 42% of a commonly accepted solar value. About 183 ppM of "organic refractory" or 200 ppM of a heavily hydrogenated carbon are required, corresponding to ZISM/Zsun = 0.88 and 0.95, respectively. If ZISM/Zsun <0.81, one or more of the basic observational parameters [the A(V)/N(H) of the diffuse ISM, the cosmic C/H ratio, or the C/H in the gaseous ISM] must be changed from its currently accepted best value. When all of the basic parameters are relaxed by 1 σ, an AMC model can fit ZISM/Zsun = 0.68. Models with AMC in the composite grains fit ZISM/Zsun = 0.58 if the parameters are relaxed by 2 σ. Compact grains (no vacuum) and those with 80% vacuum require more solid materials than those with 45% vacuum. If the Sun is, indeed, richer in heavy elements than the ISM, this paper strengthens the evidence from interstellar polarization that large interstellar grains are not extremely fluffy. The strengths of the 9.7 and 18 μm "silicate" bands provide a serious objection to the assumption that all elements are reduced uniformly from solar abundances. They seem to require at least the solar abundance of Si. Possibly some oxides can alleviate this problem.