Alfvénic turbulence in the fast solar wind is imbalanced: the energy of the (dominant) waves propagating outward from the Sun is much larger than energy of inward-propagating (subdominant) waves. At large scales Alfvén waves are non-dispersive and turbulence is driven by non-linear interactions of counter-propagating waves. Contrary to this, at kinetic scales Alfvén waves become dispersive and non-linear interactions become possible among co-propagating waves as well. The study of the transition between these two regimes of Alfvénic turbulence is important for understanding of complicated dynamics of imbalanced Alfvénic turbulence. In this paper, we present a semiphenomenological model of the imbalanced Alfvénic turbulence accounting for the energy exchange between the dominant and subdominant wave fractions. The energy transfer becomes non-negligible at sufficiently small yet still larger than the ion gyroradius scales and is driven by the non-linear beatings between dispersive dominant(subdominant) waves pumping energy into the subdominant(dominant) component. Our results demonstrate that the turbulence imbalance should decrease significantly in the weakly dispersive wavenumber range.