XML has become a standard for document storage and interchange and its convenient syntax improves the interoperability of many applications. The computational complexity and practical cost of XPath queries can vary dramatically so its unconstrained use leads to unpredictable space and time costs. Stream-processing of XPath queries mitigates this problem by restricting the query language fragment and allows simpler implementations by stack automata with no limit on the XML document size. We have designed an accurate performance model for such algorithms. It collects static information about the XML document to statically predict the memory consumption of a query to within a few percent. The model is portable, adapts to any document structure and scales to 1GiB documents and beyond. In addition to predictable performance, user interaction with the system can lead to optimizations by constraining the search for sub-documents. Existing literature on this problem has not addressed all the technical problems involved and our model is to our knowledge the most complete of its kind.