Traceroute is widely used, from the diagnosis of network problems to the assemblage of internet maps. However, there are a few serious problems with this tool, in particular due to the presence of load balancing routers in the network. This paper describes a number of anomalies that arise in nearly all traceroute-based measurements. We categorize them as “loops”, “cycles”, and “diamonds”. We provide a new publicly-available traceroute, called Paris traceroute, which controls packet header contents to obtain a more precise picture of the actual routes that packets follow. This new tool allows us to find conclusive explanations for some of the anomalies, and to suggest possible causes for others. Categories and Subject Descriptors: C.2.3 [Computer Communication Networks]: Network Operations General Terms: Measurement.