  We consider a large class of Ramsey interferometry protocols which are
enhanced by squeezing and un-squeezing operations before and after a phase
signal is imprinted on the collective spin of $N$ particles. We report an
analytical optimization for any given particle number and strengths of
(un-)squeezing. These results can be applied even when experimentally relevant
decoherence processes during the squeezing and un-squeezing interactions are
included. Noise between the two interactions is however not considered in this
work. This provides a generalized characterization of squeezing echo protocols,
recovering a number of known quantum metrological protocols as local
sensitivity maxima, thereby proving their optimality. We discover a single new
protocol. Its sensitivity enhancement relies on a double inversion of
squeezing. In the general class of echo protocols, the newly found
over-un-twisting protocol is singled out due to its Heisenberg scaling even at
strong collective dephasing.
