  Within the quantum phase representation we derive Heisenberg limits, in
closed form, for N00N states and two other classes of states that can perform
better in terms of local performance metrics relevant for multiply-peaked
distributions. One of these can also enhance the super-resolution factor beyond
that of a N00N state of the same power, at the expense of diminished fringe
visibility. An accurate phase estimation algorithm, which can be applied to the
minimally resourced apparatus of a standard interferometer, is shown to be
resilient to the presence of additive white-Gaussian noise (AWGN). In the limit
of no AWGN the algorithm achieves over nine digits of accuracy for the case of
a four-photon N00N state - orders of magnitude below its Heisenberg limit.
