This work considers data structures based on multi-party computation (MPC) primitives: structuring secret (e.g. secret shared and potentially unknown) data such that it can both be queried and updated efficiently. Implementing an oblivious RAM (ORAM) using MPC allows any existing data structure to be realized using MPC primitives, however, by focusing on a specific example -- a priority queue -- it is shown that it is possible to achieve much better results than the generic solutions can provide. Moreover, the techniques differ significantly from existing ORAM constructions. Indeed it has recently been shown that any information theoretically secure ORAM with n memory locations requires at least log n random bits per read/write to hide the access pattern. In contrast, the present construction achieves security with a completely deterministic access pattern.