Arguments formulated in a natural or scientific language usually allow for various different reconstructions. Alternative reconstructions may pertain to different approaches to inference and argumentation (such as classical predicate logic, Bayesian epistemology and many others). However, how are we to select one from among various available reconstructions? The paper provides an analysis of three different reconstructions of a particular argument and discusses their pros and cons with respect to several logical and extra-logical properties. Moreover, the three potential selection principles are considered. It is argued that they work adequately only when subjected to a specific aim of the context of argument reconstruction.