Abstract: Because of spatially inhomogeneous sources, Alfvénic turbulence in space is usually imbalanced: amplitudes of waves propagating parallel and anti-parallel to the mean magnetic field are unequal. Collisions between counter-propagating Alfvén waves have been commonly accepted as a fundamental process governing the turbulence. I show that this is not true at ion kinetic scales where the turbulence is controlled by the collisions among co-propagating dispersive Alfvén waves (co-collisions) rather than among counter-propagating ones (counter-collisions). The co-collisions dominate beyond the spectral break scale that is significantly larger than the ion gyroradius. A new quasi-inertial range of turbulence arises between the spectral break and ion gyroradius, where the co-collisions generate steepest non-universal spectra. The spectral indexes vary around >-3 (>-4) in the strong (weak) turbulence, such that steeper spectra follow larger imbalances. Our theoretical predictions are compatible with steep variable spectra observed recently at ion kinetic scales in the solar wind.