  It is shown that the addition of down-converted photon pairs to coherent
laser light enhances the N-photon phase sensitivity due to the quantum
interference between components of the same total photon number. Since most of
the photons originate from the coherent laser light, this method of obtaining
non-classical N-photon states is much more efficient than methods based
entirely on parametrically down-converted photons. Specifically, it is possible
to achieve an optimal phase sensitivity of about delta phi^2=1/N^(3/2), equal
to the geometric mean of the standard quantum limit and the Heisenberg limit,
when the average number of down-converted photons contributing to the N-photon
state approaches (N/2)^(1/2).
