Abstract. Since the introduction of interpolants to the field of symbolic model checking, interpolation-based methods have been successfully used in both hardware and software model checking. Recently, variable assignments have been introduced to the computation of interpolants. In the context of abstract reachability graphs, variable assignment can be used not only to prevent out-of-scope variables from appearing in interpolants, but also to reduce the size of the interpolant significantly. We further extend the framework for computing interpolants under variable assignment, prove the correctness of the system and show that it has potential to further decrease the size of the computed interpolants. At the end we analyze under which conditions the computed interpolants will still have the path interpolation property, a desired property in many interpolation-based techniques. 1