  We consider general three-mode interferometers using a spin-1 atomic
Bose-Einstein condensate with macroscopic magnetization. We show that these
interferometers, combined with the measurement of the number of particles in
each output port, provide an ultra-high phase sensitivity. We construct
effective two-mode interferometers which involve two Zeeman modes showing that
they also provide an ultra-high phase sensitivity but of a bit reduced factor
in the corresponding Fisher information. A special case of zero magnetization
is shown to persist the efficiency of the two-mode interferometry.
