Abstract We present a method to decompose a declarative knowledge base, given by a logic program under Answer Set Semantics with access to external sources. It overcomes the ineffectiveness of current methods due to a lack of structural information about these sources, viewed as black boxes, by exploiting independency information in accesses to them. To this end, we develop a generic notion of domain independence that allows to restrict the evaluation domain and, as a consequence, to prune unnecessary dependency assumptions between atoms. This leads to increased decomposability; we demonstrate this by an evaluation method for HEX-programs based on program rewriting, which may yield large performance gains. While developed for a particular formalism, the notions and ideas of this paper might be adapted to related formalisms as well