A highly skewed microdata contains some sensitive attribute values that occur far more frequently than others. Such data violates the "eligibility condition" assumed by existing works for limiting the probability of linking an individual to a specific sensitive attribute value. Specifically, if the frequency of some sensitive attribute value is too high, publishing the sensitive attribute alone would lead to linking attacks. In many practical scenarios, however, this eligibility condition is violated. In this paper, we consider how to publish microdata under this case. A natural solution is "minimally" suppressing "dominating" records to restore the eligibility condition. We show that the minimality of suppression may lead to linking attacks. To limit the inference probability, we propose a randomized suppression solution. We show that this approach has the least expected suppression in a large family of randomized solutions, for a given privacy requireme...