This paper studies privacy in the context of complex decision support queries composed of multiple conditions on different aggregate statistics combined using disjunction and conjunction operators. Utility requirements for such queries necessitate the need for private mechanisms that guarantee a bound on the false negative and false positive errors. This paper formally defines complex decision support queries and their accuracy requirements, and provides algorithms that proportion the existing budget to optimally minimize privacy loss while supporting a bounded guarantee on the accuracy. Our experimental results on multiple real-life datasets show that our algorithms successfully maintain such utility guarantees, while also minimizing privacy loss.