In this paper, we consider the exact top-k query problem in wireless sensor networks, i.e., where one seeks to find the k highest reported values as well as the complete set of nodes that reported them. Our primary contribution in this context is EXTOK, a provably correct and topology-independent new filtering-based algorithm for processing exact top-k queries. As a secondary contribution we confirm a previous result of ours by showing that the efficiency of top-k query processing algorithms, including EXTOK, can be further improved by simply choosing a proper underlying logical tree topology. We examine EXTOK's performance with respect to a number of parameters and different logical tree topologies while using both synthetic and real data sets. Our simulation reveal that EXTOK consistently outperforms the current state-of-the-art algorithm by a very significant margin and regardless of the underlying logical tree topology.