This paper focuses on "router-based" defense mechanisms, and whether they can provide effective solutions to network Denial-of-Service (DoS) attacks. Router-based defenses operate either on traffic aggregates or on individual flows, and have been shown, either alone or in combination with other schemes, e.g., traceback, to be reasonably effective against certain types of basic attacks. Those attacks are, however, relatively brute-force, and usually accompanied by either significant increases in congestion, and/or traffic patterns that are easily identified. It is, therefore, unclear if router-based solutions are viable in the presence of more diverse or sophisticated attacks. As a result, even if incorporating defense mechanisms in the routers themselves has obvious advantages, such schemes have not seen wide deployments. Our ultimate goal is to determine whether it is possible to build router-based defense mechanisms that are effective against a wide range of attacks. This paper describes a first phase of this effort aimed at identifying weaknesses in existing systems. In particular, the paper demonstrates that aggregate defense systems can be readily circumvented, even by a single attacker, through minor modifications of its flooding patterns. Flow-based defenses fare slightly better, but can still be easily fooled by a small number of attackers generating transient flooding patterns. The findings of the paper provide insight into possible approaches for designing better and more robust router-based defense systems.