The streaming evaluation is a popular way of evaluating queries on XML documents. Besides its many advantages, it is also the only option for a number of important XML applications. Unfortunately, existing algorithms focus almost exclusively on tree-pattern queries (TPQs). Requirements for flexible querying of XML data have motivated recently the introduction of query languages that are more general and flexible than TPQs. We consider a partial tree-pattern query (PTPQ) language which generalizes and strictly contains TPQs. PTPQs can express a fragment of XPath which comprises reverse axes and the node identity equality (is) operator, in addition to forward axes, wildcards and predicates. We outline an original streaming algorithm for PTPQs. Our algorithm is the first one to support the streaming evaluation of such a broad fragment of XPath.