The concurrent maintenance of two visual working memory (VWM) arrays can lead to profound interference. It is unclear, however, whether these costs arise from limitations in VWM storage capacity (Fougnie & Marois, 2006) or from interference between the storage of one visual array and encoding or retrieval of another visual array (Cowan & Morey, 2007). Here, we show that encoding a VWM array does not interfere with maintenance of another VWM array unless the two displays exceed maintenance capacity (Experiments 1 and 2). Moreover, manipulating the extent to which encoding and maintenance can interfere with one another had no discernable effect on dual-task performance (Experiment 2). Finally, maintenance of a VWM array was not affected by retrieval of information from another VWM array (Experiment 3). Taken together, these findings demonstrate that dual-task interference between two concurrent VWM tasks is due to a capacity-limited store that is independent from encoding and retrieval processes.