Speech foundation models, such as HuBERT and its variants, are pre-trained on large amounts of unlabeled speech for various downstream tasks. These models use a masked prediction objective, where the model learns to predict information about masked input segments from the unmasked context. The choice of prediction targets in this framework can influence performance on downstream tasks. For example, targets that encode prosody are beneficial for speaker-related tasks, while targets that encode phonetics are more suited for content-related tasks. Additionally, prediction targets can vary in the level of detail they encode; targets that encode fine-grained acoustic details are beneficial for denoising tasks, while targets that encode higher-level abstractions are more suited for content-related tasks. Despite the importance of prediction targets, the design choices that affect them have not been thoroughly studied. This work explores the design choices and their impact on downstream task performance. Our results indicate that the commonly used design choices for HuBERT can be suboptimal. We propose novel approaches to create more informative prediction targets and demonstrate their effectiveness through improvements across various downstream tasks.