Security-Aware Query Processing is the problem of computing answers to queries in the presence of access control policies. We present general impossibility results for the existence of optimal algorithms for Security-Aware Query Processing and classify query languages for which such algorithms exist. In particular, we show that for the relational calculus there are no optimal algorithms, whereas optimal algorithms exist for some of its fragments, such as the existential fragment. We also establish relationships between two different models of Fine-Grained Access Control, called Truman and Non-Truman models, which have been previously presented in the literature as distinct. For optimal Security-Aware Query Processing, we show that the Non-Truman model is a special case of the Truman model for boolean queries in the relational calculus, whereas the two models coincide for more powerful languages, such as the relational calculus with aggregation operators. In contrast, these two models are distinct for non-boolean queries.