So far P300-speller design has put very little emphasis on the design of optimized flash patterns, a surprising fact given the importance of the sequence of flashes on the selection outcome. Previous work in this domain has consisted in studying consecutive flashes, to prevent the same letter or its neighbors from flashing consecutively. To this effect, the flashing letters form more random groups than the original row-column sequences for the P300 paradigm, but the groups remain fixed across repetitions. This has several important consequences, among which a lack of discrepancy between the scores of the different letters. The new approach proposed in this paper accumulates evidence for individual elements, and optimizes the sequences by relaxing the constraint that letters should belong to fixed groups across repetitions. The method is inspired by the theory of Restricted Isometry Property matrices in Compressed Sensing, and it can be applied to any display grid size, and for any target flash frequency. This leads to P300 sequences which are shown here to perform significantly better than the state of the art, in simulations and online tests.