Packet measurements at scale are essential for several applications, such as cyber-security, accounting and troubleshooting. They, however, threaten users’ privacy by exposing sensitive information. Anonymization has been the answer to this challenge, i.e., replacing sensitive information with obfuscated copies. Anonymization of packet traces, however, comes with some challenges and drawbacks. First, it reduces the value of data. Second, it requires to consider diverse protocols because information may leak from many non-encrypted fields. Third, it must be performed at high speeds directly at the monitor, to prevent private data from leaking, calling for real-time solutions. We present <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -MON, a flexible tool for privacy-preserving packet monitoring. It replicates input packet streams to different consumers while anonymizing protocol fields according to flexible policies that cover all protocol layers. Beside classic anonymization mechanisms such as IP address obfuscation, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -MON supports <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${z}$ </tex-math></inline-formula> -anonymization, a novel solution to obfuscate rare values that can be uniquely traced back to limited sets of users. Differently from classic anonymization approaches, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z-anonymity</i> works on a streaming fashion, with zero delay, operating at high-speed links on a packet-by-packet basis. We quantify the impact of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z-anonymity</i> on traffic measurements, finding that it introduces minimal error when it comes to finding heavy-hitter services. We evaluate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -MON performance using packet traces collected from an ISP network and show that it achieves a sustainable rate of 40 Gbit/s on a Commercial Off-the Shelf server. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -MON is available to the community as an open-source project.