A Safety Case's argument is conventionally presented as a tree with claims, strategies and evidence as nodes. The level of confidence in each node and linkage can be added and an estimate of the confidence in the top-level claim calculated. Sensitivity analysis can then highlight nodes where increased confidence would significantly improve the confidence in the top-level claim — allowing work to be focused. However, the tree structure does not show how a single factor can undermine confidence in different branches of the argument. This paper describes how adding annotations to a Safety Case can extend the sensitivity analysis to detect brittle parts of the argument.