Algorithms, data structures, coding techniques, and other methods that reduce bit-flips are being sought to best utilize hardware where flipping bits is the dominating cost. Write efficient memories were introduced by Ahlswede and Zhang as a model for storage systems with these kinds of arbitrary read, write, and update costs. The introduction of non-volatile Random Access Memories like phase-change RAM, which have asymmetric read-write costs has re-motivated the field. Our work focuses on potential bit-flip efficiencies to be gained at the data structure layer. We examine Local Order Agnostic Data Structures (LOADS), data structures in which local order does not convey information and in which cells are modified individually. We found that because these data structures have a limited set of valid values and transitions, that bit flipping wins should be possible without the use of additional hardware.