Traffic inspection is a fundamental building block of many security solutions today. For example, to prevent the leakage or exfiltration of confidential insider information, as well as to block malicious traffic from entering the network, most enterprises today operate intrusion detection and prevention systems that inspect traffic. However, the state-of-the-art inspection systems do not reflect well the interests of the different involved autonomous roles. For example, employees in an enterprise, or a company outsourcing its network management to a specialized third party, may require that their traffic remains confidential, even from the system administrator. Moreover, the rules used by the intrusion detection system, or more generally the configuration of an online or offline anomaly detection engine, may be provided by a third party, e.g., a security research firm, and can hence constitute a critical business asset which should be kept confidential. Today, it is often believed that accounting for these additional requirements is impossible, as they contradict efficiency and effectiveness. We in this paper explore a novel approach, called Privacy Preserving Inspection (PRI), which provides a solution to this problem, by preserving privacy of traffic inspection and confidentiality of inspection rules and configurations, and e.g., also supports the flexible installation of additional Data Leak Prevention (DLP) rules specific to the company.