A detailed study of the structure of zero-age horizontal-branch (ZAHB) models is studied in order to show how the hydrostatic structure of these models changes with the input parameters and determines the H-R diagram location of a given model. The properties of composite polytropes on the homology-invariant (U,V)-plane are demonstrated. A variety of test models and sequences were constructed to elucidate the underlying factors that give rise to the wide variation in HB model properties with composition. The roles of the CNO elements as nuclear catalysts and of the envelope sources, as well as the envelope helium abundance are reexamined. It is found that, for stars of a fixed range of mass arriving on the HB, the stellar distribution is determined mainly by CNO for low metallicities (Fe/H of less than about -1), but mainly by opacity sources for high metallicities. The value of Fe/H where CNO ceases to dominate depends significantly on the adopted opacity and will decrease if and when opacity estimates are revised upward.