To interpret uncertainty estimates from differentiable probabilistic models, recent work has proposed generating a single Counterfactual Latent Uncertainty Explanation (CLUE) for a given data point where the model is uncertain, identifying a single, on-manifold change to the input such that the model becomes more certain in its prediction. We broaden the exploration to examine $δ$-CLUE, the set of potential CLUEs within a $δ$ ball of the original input in latent space. We study the diversity of such sets and find that many CLUEs are redundant; as such, we propose DIVerse CLUE ($\nabla$-CLUE), a set of CLUEs which each propose a distinct explanation as to how one can decrease the uncertainty associated with an input. We then further propose GLobal AMortised CLUE (GLAM-CLUE), a distinct and novel method which learns amortised mappings on specific groups of uncertain inputs, taking them and efficiently transforming them in a single function call into inputs for which a model will be certain. Our experiments show that $δ$-CLUE, $\nabla$-CLUE, and GLAM-CLUE all address shortcomings of CLUE and provide beneficial explanations of uncertainty estimates to practitioners.