The fine-grained carbonate deposits of the Oligocene to early Miocene of Cyprus are the most characteristic example of onshore outcropping carbonate drifts. These deposits were analyzed from a sedimentological and ichnological perspective, in order to determine the origin of the lenticular bedding characteristic of such deposits. The facies at the two study sections, Tsada and Petra Tou Romiou, consist of an alternation of thin, poorly cemented, intensely bioturbated marly limestone intervals and thick cemented wackestone intervals with abundant bioturbation and “lenticular bedding.” The ichnoassemblage, comprising Zoophycos, Thalassinoides, and Planolites is attributable to the Zoophycos Ichnofacies. The alternation of intervals with medium to well-preserved traces with completely biogenically homogenized facies reflects changes in substrate consistency related to changes in bottom-current velocity or to sedimentation. The presence of lenticular-bedding-like structures in the study deposits, traditionally considered diagnostic of bottom-current action in carbonate-drift outcrops, is shown to be exclusively the result of bioturbation. In the study sections, the “lenticular bedding” is the result of the coalescence of successive Zoophycos structures, which are readily preserved because they are constructed in the historical layer. It is proposed that the overlap of abundant isolated cone-shaped burrows of Zoophycos is the origin of the putative lenticular bedding recorded in the Oligocene fine-grained carbonate deposits of Cyprus, traditionally identified as drifts. Since this bedding is not related to currents in the study sections, the consideration of these carbonate deposits of Cyprus as drifts should be reevaluated. This has crucial implications for the recognition of carbonate drift outcrops elsewhere. Onshore carbonate drift outcrops wherein lenticular bedding is the main diagnostic criterion should be revisited and evaluated ichnologically.