ABSTRACT. We revisit the static dependency pair method for termination of higher-order term rewriting. In this extended abstract, we generalise the applicability criteria for the method. Moreover, we propose a static dependency pair framework based on an extended notion of computable dependency chains that harnesses the computability-based reasoning used in the soundness proof of static dependency pairs. This allows us to propose a new termination proving technique to use in combination with static dependency pairs: the static subterm criterion.