Complex event processing (CEP) systems that evaluate queries over streams of events may face unpredictable input rates and query selectivities. During short peak times, exhaustive processing is then no longer reasonable, or even infeasible, and systems shall resort to best-effort query evaluation and strive for optimal result quality while staying within a latency bound. In traditional data stream processing, this is achieved by load shedding that discards some stream elements without processing them based on their estimated utility for the query result. We argue that such input-based load shedding is not always suitable for CEP queries. It assumes that the utility of each individual element of a stream can be assessed in isolation. For CEP queries, however, this utility may be highly dynamic: Depending on the presence of partial matches, the impact of discarding a single event can vary drastically. In this work, we therefore complement input-based load shedding with a state-based technique that discards partial matches. We introduce a hybrid model that combines both input-based and state-based shedding to achieve high result quality under constrained resources. Our experiments indicate that such hybrid shedding improves the recall by up to 14× for synthetic data and 11.4× for real-world data, compared to baseline approaches.