ABSTRACT: Shapiro, Shepard, and Wong [Phys. Rev. Lett. 62, 2377 (1989)] suggested that a scheme of multiple phase measurements, using quantum states with minimum 'reciprocal peak likelihood', could achieve a phase sensitivity scaling as 1/N_tot^2, where N_tot is the mean number of photons available for all measurements. The authors have simulated their scheme for as many as 240 measurements and have found optimum phase sensitivities for 3< N_tot<=120; a power-law fit to the simulated data yields a phase sensitivity that scales as 1/N_tot^0.82+/- 0.01. By using a combination of numerical and analytical techniques, the authors extend their results to higher values of N_tot than are accessible to the simulations; the authors find no evidence for phase sensitivities better than the benchmark 1/N_tot sensitivity of squeezed-state interferometry. They conclude that reciprocal peak likelihood is not a good measure of phase sensitivity. They discuss other factors that are important to phase sensitivity.