Complex Event Processing (CEP) deals with matching a stream of events with the query patterns to extract complex matches. These matches incrementally emerge over time while the partial matches accumulate in the memory. The number of partial matches for expressive CEP queries can be polynomial or exponential to the number of events within a time window. Hence, traditional strategies result in an extensive memory and CPU utilisation. In this paper, we revisit the CEP problem through the lens of complex queries with expressive operators (skip-till-any-match and Kleene+). Our main result is that traditional approaches, based on the partial matches' storage, are inefficient for these types of queries. We advise a simple yet efficient recomputation-based technique that experimentally outperforms traditional approaches on both CPU and memory usage.