RL-based techniques can be employed to search for prompts that, when fed into a target language model, maximize a set of user-specified reward functions. However, in many target applications, the natural reward functions are in tension with one another – for example, content preservation vs. style matching in style transfer tasks. Current techniques focus on maximizing the average of reward functions, which does not necessarily lead to prompts that achieve balance across rewards – an issue that has been well-studied in the multi-objective and robust optimization literature. In this paper, we conduct an empirical comparison of several existing multi-objective optimization techniques adapted to this new setting: RL-based discrete prompt optimization. We compare two methods optimizing the volume of the Pareto reward surface and one method that chooses an update direction that benefits all rewards simultaneously. We evaluate performance on two NLP tasks: style transfer and machine translation, each using three competing reward functions. Our experiments demonstrate that multi-objective methods that directly optimize the volume of the Pareto reward surface perform better and achieve a better balance of all rewards than those that attempt to find monotonic update directions.