We seek to answer the following question: To what extent can we deduplicate replicated storage ? To answer this question, we design ReDup, a secure storage system that provides users with strong integrity, reliability, and transparency guarantees about data that is outsourced at cloud storage providers. Users store multiple replicas of their data at different storage servers, and the data at each storage server is deduplicated across users. Remote data integrity mechanisms are used to check the integrity of replicas. We consider a strong adversarial model, in which collusions are allowed between storage servers and also between storage servers and dishonest users of the system. A cloud storage provider (CSP) could store less replicas than agreed upon by contract, unbeknownst to honest users. ReDup defends against such adversaries by making replica generation to be time consuming so that a dishonest CSP cannot generate replicas on the fly when challenged by the users.