Providing consistent and fault-tolerant distributed object services is among the fundamental problems in distributed computing. To achieve fault-tolerance and to increase throughput, objects are replicated at different networked nodes. However, replication induces significant communication costs to maintain replica consistency. Eventually-Serializable Data Service (ESDS) has been proposed to reduce these costs and enable fast operations on data, while still providing guarantees that the replicated data will eventually be consistent. This paper revisits ESDS instances where bandwidth constraints are imposed on segments of the network interconnect. This class of problems was shown to be extremely challenging for both Mixed Integer Programming (MIP) and for Constraint Programming (CP), some instances requiring hours of computation time. The paper presents an improved constraint programming model, a constraint-based local search model that can obtain high-quality solutions quickly and a local search/constraint programming hybrid. The experimental results indicate that the resulting models significantly improve the state of the art.