We discuss theoretically a frustrated Heisenberg antiferromagnet in magnetic field close to the saturation one. It is demonstrated that a small biaxial anisotropy and/or the magnetic dipolar interaction produce a delicate balance between phases with a commensurate canted, incommensurate helical (conical), and fan spin orderings. As a result, different sequences of phase transitions are realized depending on values of these small anisotropic interactions. We derive analytical expressions for critical fields and ground-state energies of the phases which are in a quantitative agreement with our and previous Monte-Carlo simulations.