Representations of visual objects in working memory (WM) can be part-based or object-based, and we investigated whether this is determined by top-down control processes. Lateralised change detection tasks were employed where sample objects on one task-relevant side had to be memorized. Contralateral delay activity (CDA) components were measured during the retention period as electrophysiological markers of WM maintenance processes. In two critical task conditions, sample displays contained objects composed of two vertically aligned shapes. In the Parts task, test displays contained a single shape that had to be matched with either of the two sample shapes, encouraging the storage of part-based WM representations. In the Whole task, compound-shape objects shown at test had to be matched with memorized compound objects, which should facilitate the formation of object-based integrated WM representations. CDA amplitudes were significantly larger in the Parts task than in the Whole task, indicative of differences in effective WM load. This suggests that the two individual shapes were represented separately in the Parts task, whereas a single compound object was maintained in the Whole task. These results provide new evidence that changes in task goals can result in qualitative differences in the way that identical visual stimuli are represented in WM.