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Although the electric conductivity of ionic solutions is of great importance in science and technology, complete understanding of the physical factors and principles underlying ion and charge transport in solution has so far been missing. The Debye–Hückel–Onsager (DHO) theory of the equivalent ionic conductivity (λi for single ion i, Λ for a binary electrolyte) is a limiting law of only a few electrolyte valence families, and its extension to solution of finite concentration has not been entirely successful; at most, it has led to semiempirical expressions of λi or Λ vs. concentration (c), incorporating adjustable parameters of no clear physical meaning. Improving the description of the ion atmosphere and including in the conductivity model the smaller-ion shell (SiS) of this atmosphere (D. Fraenkel, Mol. Phys., 2010, 108, 1435) allow now an extension of the DHO theory to a “DHO-SiS” theory that offers analytic expressions for λi and Λ as a function of c without adjustable parameters. The fit with experiment is very good, often excellent, for many electrolytes of the various valence families. λi values can be converted to single-ion activity coefficients, γis, suggesting that the latter ionic factors do have physical validity, contrary to what many literature sources claim. Together with the recently proposed theory of the limiting conductivities, λ0i and Λ0 (D. Fraenkel, Mol. Phys., 2018, 116, 2271), the new theory offers a simple and comprehensive ion conductivity treatment that improves upon existing theoretical treatments, with λi and Λ expressed by ionic sizes instead of λ0i and Λ0. [ABSTRACT FROM AUTHOR]