Several research lines attempted to tell truthful from deceptive texts by looking at the concreteness in language as an indicator of truthfulness. We identified eight different operationalizations of concreteness for computer-automated analysis and validated these operationalizations on six diverse datasets containing truthful and deceptive texts (about hotel reviews, past and future weekend plans, as well as intended flight plans). The results suggest that not just the efficacy but also the directionality of concreteness as a cue to deception is dependent on the operationalization and the context. A predictive analysis suggests that concreteness indices can differentiate between truthful and deceptive statements above the chance level and are a worthy path for future research. The importance of conducting multi-dataset and multi-operationalization investigations in linguistic deception detection research is highlighted.