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We consider the problem of designing multipulse pulse-position modulation (MPPM) constellations whose sizes are powers of two. This problem amounts to selecting a subset from the collection of all (wn) possible signal points of MPPM with w pulses in n time slots. In a previous work, we have tackled this selection using combinatorial heuristics. In this letter, we further explore two new continuous optimization approaches. The first one is a modified Blahut-Arimoto algorithm. The second one is inspired from compressed sensing. Using the constellation-constrained channel capacity as the figure of merit, numerical results from a relevant free-space optical communication example suggest that simple combinatorial heuristics yield practically the best designs.