  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 ($-\pi/2,
\pi/2$).
