Neighbourhoods of precise probabilities are instrumental to perform robustness analysis, as they rely on very few parameters. In the rst part of this study, we introduced a general, unied view encompassing such neighbourhoods, and revisited some well-known models (pari mutuel, linear vacuous, constant odds-ratio). In this second part, we study models that have received little to no attention, but are induced by classical distances between probabilities, such as the total variation, the Kolmogorov and the L 1 distances. We nish by comparing those models in terms of a number of properties: precision , number of extreme points, n-monotonicity,. .. thus providing possible guidelines to select a neighbourhood rather than another.