Operator migration is a crucial concept to adapt event processing systems to dynamic changes. When the placement of a stateful operator changes, the operator state must be migrated to the new host. However, operator state size and time constraints can make it impossible to migrate the operator without severe Quality of Service (QoS) degradation. As a relief, we propose to perform state shedding in such a situation. The core idea of state shedding is to partition the operator state, assign a utility to each partial state, and use the utility and size of each partial state to identify the most useful partial states that can be migrated in a given time frame. Thus, state shedding can maintain a substantially higher QoS with a lower impact on query results than state-of-the-art solutions targeting consistent state at the old and new host. In this paper, we define this novel approach and in a simulation environment evaluate state shedding in migration scenarios with pattern-matching queries