The input states of an interferometer have been optimized at fixed tot
al photon number N and quantum efficiency eta. I show that the phase s
ensitivity is bounded by Delta phi similar to N--3/4 for a coherent in
put signal and by Delta phi similar to N-1 for squeezed optimized inpu
ts. I also show that in actual non-efficient interferometers only litt
le squeezing is needed to reach the best sensitivity.