Identifying heavy hitter flows is a fundamental problem in various network domains. The well established method of using sketches to approximate flow statistics suffers from space inefficiencies. In addition, flow arrival rates are dynamic, thus keeping track of the most recent heavy hitters poses a challenge. Sliding window approximations address this problem, reducing space at the cost of increasing point query time. This paper presents two novel algorithms for identifying heavy hitters in streams and sliding windows. Both algorithms use statically allocated memory and support constant time point queries. For sliding windows, this is an asymptotic improvement over previous work. We also demonstrate reduced memory requirements of up to 85% in streams and 66% in sliding windows over synthetic and real Internet packet traces.