A proposed phase-estimation protocol based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that the Cram{e}r-Rao sensitivity is sub-Heisenberg [Phys. Rev. Lett. {bf104}, 103602 (2010)]. However, these measurements are problematic, making it unclear if this sensitivity can be obtained with a finite number of measurements. This sensitivity is only for phase near zero, and in this region there is a problem with ambiguity because measurements cannot distinguish the sign of the phase. Here, we consider a finite number of parity measurements, and show that an adaptive technique gives a highly accurate phase estimate regardless of the phase. We show that the Heisenberg limit is reachable, where the number of trials needed for mean photon number $bar{n}=1$ is approximately one hundred. We show that the Cram{e}r-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval ($-pi/2, pi/2$).
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