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Multimedia objects are distributed to peers through downloading and caching in peer-to-peer (P2P) overlay networks. Multimedia objects are characterized in terms of not only data structure but also quality of service (QoS). Replicas of a multimedia object are partially ordered in terms of the newness precedent relation of data structure and QoS. In the multimedia quorum-based (MQB) protocol, multiple replicas of a multimedia object are synchronized based on the newness precedent relation. An object is an encapsulation of data and abstract operations for manipulating the data. The data of an object is changed in a write type of operation. Write operations are classified into enriching and impoverishing types of operations. In an enriching operation, some data is added to a replica like an operation to increase the number of colours. On the other hand, in an impoverishing operation, some data in a replica is removed like operation to degrade QoS. If an enriching operation is issued to replicas in a quorum, every replica in the quorum is updated like the traditional quorum-based (QB) protocols. On the other hand, if an impoverishing operation is issued to a quorum, every replica in the quorum is not updated where the operations are logged to reduce communication and computation overheads. In this paper, only impoverishing operations are logged while enriching operations are performed on every replica in the quorum. Then, only impoverishing operations to be performed in a log are later performed on a replica and logged in a replica. In addition the size of the log is reduced by removing operation not to be performed.