Visual short-term memory (VSTM) is limited in the quantity and quality of items that can be retained over time. Importantly, these two mnemonic parameters interact: increasing the number of items in VSTM reduces the quality with which they are represented. Here, we ask whether this trade-off is under top-down control. Specifically, we test whether participants can strategically optimise the trade-off between quality and quantity for VSTM according to task demands. We manipulated strategic trade-off by varying expectations about the number of to-be-remembered items (Experiments 1-2) or the precision required for the memory-based judgement (Experiment 3). In a final experiment, we manipulated both variables in a complementary way to maximise the motivation to strategically control the balance between number and the quality of items encoded into VSTM. In different blocks, performance would benefit most either by encoding a large number of items with low precision or by encoding a small number of items with high precision (Experiment 4). In all experiments, we compared VSTM performance on trials matched for mnemonic demand, but within contexts emphasising the quality or quantity of VSTM representations. Across all four experiments, we found no evidence to suggest that participants use this contextual information to bias the balance between the number and precision of items in VSTM. Rather, our data suggest that the trade-off may be determined primarily by stimulus-driven factors at encoding.