In sensor networks, data acquisition frequently takes place at low-capability devices. The acquired data is then transmitted through a hierarchy of nodes having progressively increasing network band-width and computational power. We consider the problem of executing queries over these data streams, posed at the root of the hierarchy. To minimize data transmission, it is desirable to perform "in-network" query processing: do some part of the work at intermediate nodes as the data travels to the root. Most previous work on in-network query processing has focused on aggregation and inexpensive filters. In this paper, we address in-network processing for queries involving possibly expensive conjunctive filters, and joins. We consider the problem of placing operators along the nodes of the hierarchy so that the overall cost of computation and data transmission is minimized. We show that the problem is tractable, give an optimal algorithm, and demonstrate that a simpler greedy operator placement algorithm can fail to find the optimal solution. Finally we define a number of interesting variations of the basic operator placement problem and demonstrate their hardness.