A protocol is given to take an ElGamal ciphertext encrypted under the key of one distributed service and produce the corresponding ciphertext encrypted under the key of another distributed service, but without the plaintext ever becoming available. Each distributed service comprises a set of servers and employs threshold cryptography to maintain its service private key. Unlike prior work, the protocol requires no assumptions about execution speeds or message delivery delays. The protocol also imposes fewer constraints on where and when various steps are performed, which can bring improvements in end-to-end performance for some applications (e.g., a trusted publish/subscribe infrastructure.) Two new building blocks employed — a distributed blinding protocol and verifiable dual encryption proofs — could have uses beyond re-encryption protocols.