Background knowledge about the application domain can be used in event processing in order to improve processing quality. The idea of semantic enrichment is to incorporate background knowledge into events, thereby generating enriched events which, in the next processing step, can be better understood by event processing engines. In this paper, we present an efficient technique for event stream enrichment by planning multi-step event enrichment and processing. Our optimization goal is to minimize event enrichment costs while meeting application-specific service expectations. The event enrichment is optimized to avoid unnecessary event stream enrichment without missing any complex events of interest. Our experimental results shows that by using this approach it is possible to reduce the knowledge acquisition costs.