Three dual-task experiments examined the influence of processing a briefly presented visual object for deferred verbal report on performance in an unrelated auditory-manual reaction time (RT) task. RT was increased at short stimulus-onset asynchronies (SOAs) relative to long SOAs, showing that memory consolidation processes can produce a functional processing bottleneck in dual-task performance. In addition, the experiments manipulated the spatial compatibility of the orientation of the visual object and the side of the speeded manual response. This cross-task compatibility produced relative RT benefits only when the instruction for the visual task emphasized overlap at the level of response codes across the task sets (Experiment 1). However, once the effective task set was in place, it continued to produce cross-task compatibility effects even in single-task situations ("ignore" trials in Experiment 2) and when instructions for the visual task did not explicitly require spatial coding of object orientation (Experiment 3). Taken together, the data suggest a considerable degree of task-set inertia in dual-task performance, which is also reinforced by finding costs of switching task sequences (e.g., AC --> BC vs. BC --> BC) in Experiment 3.