Most encrypted data formats leak metadata via their plaintext headers, such as format version, encryption schemes used, number of recipients who can decrypt the data, and even the recipients’ identities. This leakage can pose security and privacy risks to users, e.g., by revealing the full membership of a group of collaboators from a single encrypted e-mail, or by enabling an eavesdropper to fingerprint the precise encryption software version and configuration the sender used. We propose that future encrypted data formats improve security and privacy hygiene by producing Padded Uniform Random Blobs or PURBs: ciphertexts indistinguishable from random bit strings to anyone without a decryption key. A PURB’s content leaks nothing at all, even the application that created it, and is padded such that even its length leaks as little as possible. Encoding and decoding ciphertexts with no cleartext markers presents efficiency challenges, however. We present cryptographically agile encodings enabling legitimate recipients to decrypt a PURB efficiently, even when encrypted for any number of recipients’ public keys and/or passwords, and when these public keys are from different cryptographic suites. PURBs employ Padmé, a novel padding scheme that limits information leakage via ciphertexts of maximum length M to a practical optimum of O(loglog M) bits, comparable to padding to a power of two, but with lower overhead of at most 12% and decreasing with larger payloads.