The question of whether visual working memory (VWM) stores individual features or bound objects as basic units is actively debated. Evidence exists for both feature-based and object-based storages, as well as hierarchically organized representations maintaining both types of information at different levels. One argument for feature-based storage is that features belonging to different dimensions (e.g., color and orientations) can be stored without interference suggesting independent capacities for every dimension. Here, we studied whether the lack of cross-dimensional interference reflects genuinely independent feature storages or mediated by common objects. In three experiments, participants remembered and recalled the colors and orientations of sets of objects. We independently manipulated set sizes within each feature dimension (making colors and orientations either identical or differing across objects). Critically, we assigned to-be-remembered colors and orientations either to same spatially integrated or to different spatially separated objects. We found that the precision and recall probability within each dimension was not affected by set size manipulations in a different dimension when the features belonged to integrated objects. However, manipulations with color set sizes did affect orientation memory when the features were separated. We conclude therefore that different feature dimensions can be encoded and stored independently but the advantage of the independent storages are mediated at the object-based level. This conclusion is consistent with the idea of hierarchically organized VWM.