Researchers use fixation identification algorithms to parse eye movement trajectories into a series of fixations and saccades, simplifying analyses and providing measures which may relate to cognition. The Distance Dispersion (I-DD) a widely-used elementary fixation identification algorithm. Yet the ”optimality” properties of its most popular greedy implementation have not been described. This paper: (1) asks how ”optimal” should be defined, and advances maximizing total fixation time and minimizing number of clusters as a definition; (2) asks whether the greedy implementation of I-DD is optimal, and shows that it is when no fixations are rejected for being too short; and (3) we show that when fixation time rejection criterion are enabled, the greedy algorithm is not optimal. We propose an O(n) algorithm which is.