  We consider 2D Heisenberg antiferromagnets on a triangular lattice with
spatially anisotropic interactions in a high magnetic field close to the
saturation. We show that this system possess rich phase diagram in
field/anisotropy plane due to competition between classical and quantum orders:
an incommensurate non-coplanar spiral state, which is favored classically, and
a commensurate co-planar state, which is stabilized by quantum fluctuations. We
show that the transformation between these two states is highly non-trivial and
involves two intermediate phases -- the phase with co-planar incommensurate
spin order and the one with non-coplanar double-${\bf Q}$ spiral order. The
transition between the two co-planar states is of commensurate- incommensurate
type, not accompanied by softening of spin-wave excitations. We show that a
different sequence of transitions holds in triangular antiferromagnets with
exchange anisotropy, such as Ba3CoSb2O9.
