Extending description logics with so-called nominal schemas has been shown to be a major step towards integrating description logics with rules paradigms. However, establishing efficient algorithms for reasoning with nominal schemas has so far been a challenge. In this paper, we present an algorithm to reason with the description logic fragment ELROVn, a fragment that extends EL++ with nominal schemas. We also report on an implementation and experimental evaluation of the algorithm, which shows that our approach is indeed rather efficient.