Recent work has shown that the adversary’s background knowledge is a very important factor in privacy-preserving data publishing. In this paper, we formalize background knowledge ħ of form “an individual X’s sensitive value belongs to class C or range R”. Through analyzing the drawbacks of previous approaches in dealing with this form of background knowledge, we develop a novel privacy criterion (τ, λ)-uniqueness that sufficiently defends against attacks leveraging the background knowledge ħ. We accompany the criterion with an effective algorithm, which computes a privacy-guarded published table that permits retrieval of accurate aggregate information about the microdata. We illustrate its advantages through theoretical analysis and experimental validation.