Distributed Constraint Optimization (DCOP) is rapidly emerging as a prominent technique for multiagent coordination. However, despite agent privacy being a key motivation for applying DCOPs in many applications, rigorous quantitative evaluations of privacy loss in DCOP algorithms have been lacking. Recently, Maheswaran et al. introduced a framework for quantitative evaluations of privacy in DCOP algorithms, showing that some DCOP algorithms lose more privacy than purely centralized approaches and questioning the motivation for applying DCOPs. This paper addresses the question of whether state-of-the art DCOP algorithms suffer from a similar shortcoming by investigating several of the most efficient DCOP algorithms, including both DPOP and ADOPT. Furthermore, while previous work investigated the impact on efficiency of distributed contraint reasoning design decisions (e.g. constraint-graph topology, asynchrony, message-contents), this paper examines the privacy aspect of such decisions, providing an improved understanding of privacy-efficiency tradeoffs.