Cognitive efficiency (CE) is generally defined as qualitative increases in knowledge gained in relation to the time and effort invested in knowledge acquisition. Across disciplines, limited consensus exists concerning the conceptual and measurement properties of CE partly because some researchers indiscriminately use the construct of CE to describe neurological, instructional, performance, and learning efficiency. In this study, two models of measuring CE, the "likelihood" model (Hoffman & Schraw, 2010), and the "deviation" model ([32] and [65]) were used to compare problem-solving outcomes and determine if different conceptual models of CE measure the same or different efficiency constructs. The two models yielded uncorrelated scores using the same data. Further, regression analysis revealed that unique variance associated with effort, self-efficacy judgments, and background knowledge differed according to the measurement model used, suggesting that either each measurement approach assessed a different facet of CE, or the efficiency constructs measured were altogether different. Practical applications of CE research for teaching and learning are discussed. (Contains 6 tables.)