Convex sets of probabilities are general models to describe and reason with uncertainty. Moreover, robust decision rules defined for them enable one to make cautious inferences by allowing sets of optimal actions to be returned, reflecting lack of information. One caveat of such rules, though, is that the number of returned actions is only bounded by the number of possibles actions, which can be huge, such as in combinatorial optimisation problems. For this reason, we propose and discuss new decision rules whose number of returned actions is bounded by a fixed value and study their consistency and numerical behaviour.