Following previous studies by Milburn and Braunstein, and Cochrane, Milburn, and Munro, we consider number-phase teleportation protocols. We investigate the use, as the teleportation quantum channel, of two-mode states with a perfectly well defined phase difference and number sum, which are also suitable for Heisenberg-limited interferometry. We show that intuition based on squeezing of these variables, which is commonly used to derive entangled states using the EPR paradox, can fail in this case to yield suitable teleportation channels. We show that the domain of failure is in fact of size 1/N, N being the total number of photons. We also point out another way of generating simpler analogs of number-sum/phase-difference eigenstates.