Ion dynamics effects and the resulting dispersed frequency response of conducting materials have often been explained in the past by a combination of the Moynihan original modulus formalism (OMF) and the Ngai coupling model (NCM). These incorrect approaches and their inappropriate conclusions are replaced by alternate, Kohlrausch-related physically reasonable conductive-system fitting and interpretation models that are then used for the analysis of both limited-range and wide-range data for the supercooled liquid 0.4Ca(NO3)(2)center dot 0.6KNO(3) (CKN). Detailed analysis of the limited-range 342 K data at the electric modulus immittance level shows that OMF fitting leads to an excess wing and that more appropriate models fit the data well without such a wing. Further, although such models allow estimation of the bulk dipolar dielectric constant of the material, as well as one associated only with mobile charges, they lead to implausibly small estimates of the important Kohlrausch K1 model shape parameter, beta(1), and lead to an inadequate determination of its characteristic relaxation time. Therefore, wide-range CKN data sets extending to nearly 10(12) Hz for the temperatures 342, 350, 356, and 361 K were very well-fitted with a more detailed composite model but one still involving K1 response. All model parameters were well-determined with no excess wings; beta(1) estimates were all much closer to the universal value of 1/3; and the estimated model parameters led to a Boson peak beyond 10(12) Hz, to very large thermal activation energies, and to evidence that the mobile charge concentration reached a saturation value at about 356 K. Such results do not support assumptions about variable ion-ion correlation, a mainstay of the OMF and NCM approaches. Finally, it is shown that although excess wings can sometimes be eliminated by using just an appropriate bulk fitting model and series blocking-electrode capacitor, as shown for the present narrow-range data, adequate fitting of the present wide-range data sets over their full spans of as much as 13 decades required the addition of an additional series dispersive-response model to the composite model. This addition seems likely to be required to take adequate account of the presence of more than one species of mobile charge in CKN.