Most flooding experiments in sandstone cores are carried out either in almost homogeneous samples or in core samples of uncertain heterogeneity. As a result, the interaction of small-scale sedimentary heterogeneity with the fluid mechanics of water-oil displacement cannot be adequately understood or quantified. Because most elastic sediments show some degree of lamination, this might be expected to have a significant influence on both oil displacement efficiency and residual/remaining oil saturation. This paper reports results from low-rate, drainage/imbibition floods in a 20 x 10 x 1-cm water-wet slab of cross-laminated heterogeneous eolian sandstone. The distribution of porosity, permeability, initial water saturation and residual oil saturation were monitored with computerized-tomography (CT) scanning techniques. The low-rate imbibition floods show that between 30% and 55% of original oil may be trapped in isolated high-permeability lamina. This work shows the importance of recognizing the role of core-scale heterogeneity in the laboratory measurement of waterflood behavior (i.e., the interaction of capillary forces with rock structure, particularly lamination). The practice of performing high-rate floods on rock samples assumed to be homogeneous is unwise and can lead to erroneous conclusions. The results of this work have major implications for (1) two-phase petrophysical measurements; (2) assessment of residual/ remaining oil, and (3) multiphase-flow scaleup.