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Attribute-based methods are inherently identity-less as authorization decisions are made in terms of attributes possessed by the subject rather than identity. However, anonymity against the system is not guaranteed when attribute distribution allows for the composition of a policy that few subjects can satisfy. An anonymizing array ensures that any assignment of values to t attributes that appears in the array appears at least r times. When an anonymizing array is used for subjects registered to a system and policies contain conjunctions of at most t attributes, the system cannot identify the subject using the policy to to gain authorization with greater than 1𝑟 probability. Anonymizing arrays are similar to covering arrays with higher coverage and constraints, but have an additional desired property, homogeneity, due to their application domain. In this paper, we develop constructions for anonymizing arrays and propose a post-optimization mechanism to reduce homogeneity.