It is known that no algorithm can extract the minimal depleting Σ-module from ontologies in expressive description logics (DLs). Thus research has focused on algorithms that approximate minimal depleting modules ‘from above’ by computing a depleting module that is not necessarily minimal. The first contribution of this paper is an implementation (AMEX) of such a depleting module extraction algorithm for expressive acyclic DL ontologies that uses a QBF solver for checking conservative extensions relativised to singleton interpretations. To evaluate AMEX and other module extraction algorithms we propose an algorithm approximating minimal depleting modules ‘from below’ (which also uses a QBF solver). We present experiments based on NCI (the National Cancer Institute Thesaurus) that indicate that our lower approximation often coincides with (or is very close to) the upper approximation computed by AMEX, thus proving for the first time that an approximation algorithm for minimal depleting modules can be almost optimal on a large ontology. We use the same technique to evaluate locality-based module extraction and a hybrid approach on NCI.