The study of how rivers cross obstructing mountains, once popular in the early twentieth century, has seen a dramatic resurgence in the last decade. Since Hutton's scholarly introduction to a possible cause for transverse drainage, however, no single study has compiled all of the various criteria that can be used to discriminate among the four possible mechanisms of antecedence, superimposition, overflow, and piracy. This paper presents the first such compilation and related methodology to apply these criteria both in tabular and graphical formats, as well as an online interactive tool in the data repository. Combining nominal and ordinal data sources, this methodology generates an objective, reproducible assessment for the mechanism most likely to have established the transverse drainage at five ordinal levels of confidence. When applied to southwestern U.S. sites, randomly selected through an objective spatial procedure, four general observations emerged on the relationship between the development of transverse drainage and landscape evolution. (1) Streams persisting through lengthy periods of extension develop antecedent canyons. (2) In order to reestablish through-flowing channels, streams overflow closed basins as active extension wanes. (3) Following a drop in base level related to the newly developed trunk channels, streams tributary to the trunk channels incise into basin-fill deposits—sometimes leading to the development of superimposed drainages. (4) Tributaries eroding headward, in response to the integration of two or more closed basins, can capture and redirect drainage; this permits transverse drainage through both piracy and superimposition upstream of the capture event. Because extant criteria use nominal and ordinal data almost entirely, considerable potential exists to refine this approach through future strategies that incorporate interval data. Future use of a criteria-based method has the potential to inform on prior geomorphic studies by providing a new perspective with which to study how basins evolve in active tectonic regions, the analysis of related basin sedimentation, the hydrological and biological aspects of drainage evolution, and transverse drainage found in Martian crater fields.