We present the first measurement of the scale-dependent power anisotropy of Elsasser variables in imbalanced fast solar wind turbulence. The dominant Elsasser mode is isotropic at lower spacecraft frequencies but becomes increasingly anisotropic at higher frequencies. The subdominant mode is anisotropic throughout. There are two distinct subranges exhibiting different scalings within what is normally considered the inertial range. The low Alfvén ratio and the different scaling of the Elsasser modes suggests an interpretation of the observed discrepancy between the velocity and magnetic field scalings, the total energy is dominated by the latter. These results do not appear to be fully explained by any of the current theories of incompressible imbalanced MHD turbulence.