The Adler-Adler cross-section formalism with energy-dependent parameters is a practical approximation to the R-Matrix formalism, based on the smallness of the s-wave neutron width in fissile elements. Attempts have been made to represent experimental cross sections by the Adler-Adler formulas through an initial representation by the Reich-Moore approximation of R-Matrix and a subsequent conversion of the Reich-Moore formulas to the Adler-Adler formulas. Adler and Adler had foreseen difficulties in associating their formulas with approximate R-Matrix theories such as those of Reich-Moore. Indeed, it is shown that due to the nonunitarity of the Adler-Adler formalism on the one hand and the unitarity, by definition, of the Reich-Moore formalism on the other hand, the conversion from the latter to the former is ambiguous. Examples are shown to demonstrate that this ambiguity results in numerical inaccuracies, sometimes very large ones, for neutron widths that are not extremely small. Improved Adler-Adler-type formulas have been derived from the R-Matrix formalism. In these formulas, the multipliers of the Breit-Wigner resonance lines exhibit more explicit energy dependence than their original counterparts, mainly in the form of additional terms in the formula for the total cross section. The conversion from Reich-Moore cross sections to the improved resonance formulas is shown to be much less ambiguous and to produce very accurate cross sections. In particular, the inaccuracies encountered with the Reich-Moore-Adler-Adler conversion are eliminated. A computer code, PEDRA, was written to perform the conversion from a given set of Reich-Moore parameters to the parameters required in the improved formulas. The numerical algorithm of this code is based on an adaptation with modifications of the numerical approach of de Saussure-Perez in the POLLA code, which converts Reich-Moore parameters to Adler-Adler parameters.