Despite the proliferation of detection and containment techniques in the worm defense literature, simple threshold-based methods remain the most widely deployed and most popular approach among practitioners. This popularity arises out of the simplistic appeal, ease of use, and independence from attack-specific properties such as scanning strategies and signatures. However, such approaches have known limitations: they either fail to detect low-rate attacks or incur very high false positive rates. We propose a multi-resolution approach to enhance the power of threshold-based detection and rate-limiting techniques. Using such an approach we can not only detect fast attacks with low latency, but also discover low-rate attacks - several orders of magnitude less aggressive than today?s fast propagating attacks with low false positive rates. We also outline a multi-resolution rate limiting mechanism for throttling the number of new connections a host can make, to contain the spread of worms. Our trace analysis and simulation experiments demonstrate the benefits of a multiresolution approach for worm defense.