Rewriting queries using views is a powerful technique that has applications in query optimization, data integration, data warehousing, etc. Query rewriting in relational databases is by now rather well investigated. However, in the framework of semistructured data the problem of rewriting has received much less attention. In this paper we focus on extracting as much information as possible from algebraic rewritings for the purpose of optimizing regular path queries. The cases when we can find a complete exact rewriting of a query using a set a views are very “ideal”. However, there is always information available in the views, even if this information is only partial. We introduce “lower” and “possibility” partial rewritings and provide algorithms for computing them. These rewritings are algebraic in their nature, i.e. we use only the algebraic view definitions for computing the rewritings. We do not use any pairs (tuples) of objects for computing the rewritings. This fact makes them a main memory product, which can be used for reducing secondary memory and remote access. After the main memory algebraic computation of the rewritings there is a second phase, with secondary memory access, for deriving the pairs of objects in the query answer. We give two algorithms for utilizing the partial lower and partial possibility rewritings to decrease the number of secondary memory accesses.