In spite of all of the technical progress in observed-score equating, several of the more conceptual aspects of the process still are not well understood. As a result, the equating literature struggles with rather complex criteria of equating, lack of a test-theoretic foundation, confusing terminology, and ad hoc analyses. A return to Lord's foundational criterion of equity of equating, a derivation of the true equating transformation from it, and mainstream statistical treatment of the problem of estimating the transformation for various data-collection designs exist as a solution to the problem.