Obfuscation-based private web search (OB-PWS) solutions allow users to search for information in the Internet while concealing their interests. The basic privacy mechanism in OB-PWS is the automatic generation of dummy queries that are sent to the search engine along with users' real requests. These dummy queries prevent the accurate inference of search profiles and provide query deniability. In this paper we propose an abstract model and an associated analysis framework to systematically evaluate the privacy protection offered by OB-PWS systems. We analyze six existing OB-PWS solutions using our framework and uncover vulnerabilities in their designs. Based on these results, we elicit a set of features that must be taken into account when analyzing the security of OB-PWS designs to avoid falling into the same pitfalls as previous proposals.