Controlled Query Evaluation (CQE) defines a logical framework to protect confidential information in a database. By modeling a user's a priori knowledge appropriately, a CQE system not only controls access to certain database entries but also accounts for information inferred by the user. In this article, we present a static (preprocessing) CQE-approach for propositional databases with an availability policy. The resulting inference-proof and availability-preserving database ensures confidentiality of secret information while guaranteeing availability of certain database entries to a highest degree possible. We illustrate the semantics of the system by a comprehensive example and state the essential requirements for an inference-proof and availability-preserving database. We present an algorithm that accomplishes the preprocessing by combining SAT solving and "Branch and Bound".