  Photon counting measurement has been regarded as the optimal measurement
scheme for phase estimation in the squeezed-state interferometry, since the
classical Fisher information equals to the quantum Fisher information and
scales as $\bar{n}^2$ for given input number of photons $\bar{n}$. However, it
requires photon-number-resolving detectors with a large enough resolution
threshold. Here we show that a collection of $N$-photon detection events for
$N$ up to the resolution threshold $\sim \bar{n}$ can result in the ultimate
estimation precision beyond the shot-noise limit. An analytical formula has
been derived to obtain the best scaling of the Fisher information.
