Linking network flows is an important problem in intrusion detection as well as anonymity. Passive traffic analysis can link flows but requires long periods of observation to reduce errors. Active traffic analysis, also known as flow watermarking, allows for better precision and is more scalable. Previous flow watermarks introduce significant delays to the traffic flow as a side effect of using a blind detection scheme; this enables attacks that detect and remove the watermark, while at the same time slowing down legitimate traffic. We propose the first non-blind approach for flow watermarking, called RAINBOW, that improves watermark invisibility by inserting delays hundreds of times smaller than previous blind watermarks, hence reduces the watermark interference on network flows. We derive and analyze the optimum detectors for RAINBOW as well as the passive traffic analysis under different traffic models by using hypothesis testing. Comparing the detection performance of RAINBOW and the passive approach we observe that both RAINBOW and passive traffic analysis perform similarly good in the case of uncorrelated traffic, however, the RAINBOW detector drastically outperforms the optimum passive detector in the case of correlated network flows. This justifies the use of non-blind watermarks over passive traffic analysis even though both approaches have similar scalability constraints. We confirm our analysis by simulating the detectors and testing them against large traces of real network flows.