We present a generalization of Spector's bar recursion to the Diller-Nahm variant of Gödel's Dialectica interpretation. This generalized bar recursion collects witnesses of universal formulas in sets of approximation sequences to provide an interpretation to the double-negation shift principle. The interpretation is presented in a fully computational way, implementing sets via lists. We also present a demand-driven version of this extended bar recursion manipulating partial sequences rather than initial segments. We explain why in a Diller-Nahm context there seems to be several versions of this demand-driven bar recursion, but no canonical one.