Plausible deniability is a strong cryptographic security property which, in the context of data storage, offers protection against invasive and coercive adversaries who have the power to extort the passwords to encrypted data. Concretely, to defend against such threats, the storage must be formatted in such a way that multiple passwords can be used to access it, some disclosing innocent data, others unlocking secret contents: the user can then only reveal passwords from the first set to the adversary, and plausibly deny that more exist. This problem has collected the interest of the computer security community for some time now. Several schemes have been devised over the last two decades, offering various levels of performance and security. Some of them, achieving very good performance, arguably do not provide satisfactory guarantees of deniability. Others, accomplishing full, bulletproof security, suffer instead from severe performance hits (especially in terms of I/O overhead and disk space utilisation). We propose a novel design, a scheme called Shufflecake, which targets a more balanced compromise between performance and security. The level of deniability it offers, while not protecting against attacks in the most stringent threat model, is sufficient in many practical scenarios. On the other hand, it achieves a 99.6% disk efficiency, and a 1x-3x slowdown over regular disk encryption tools, which makes it suited for real-world applications.