Given the lack of sensitization to the multi-dimensional concept of quality, and given the versatility of the concept of relevance, the present investigation attempts to examine the premise that Relevance Theory (RT) can function as a standard or a benchmark for maximizing and/or optimizing quality in CI. Whilst the theoretical part relies heavily on Ernst-August Gutt’s seminal work Translation and Relevance: Cognition and Context (2000), the practical part draws on some empirical data obtained from trainee-interpreters’ recorded sessions at the Hashemite University (Jordan) in order to provide a relevance-driven account for some semantic, syntactic, and cultural difficulties and problems in CI. The study arrives at the main conclusion that the degree of quality in CI largely depends on the degree of relevance achieved by the interpreter’s TL version, i.e., quality in CI would rise exponentially with the degree of relevance achieved by the interpreter’s TL version. The study also concludes that the pragmatic RT can be considered a reliable instrument, a reliable frame of reference, or a reliable screening system that can ensure both relevance-building and a correspondingly concomitant quality-building in CI, i.e., RT can possibly fine-tune the interpreters’ performance in the booth.