  Alfv\'enic turbulence in space is usually imbalanced: amplitudes of waves
propagating parallel and anti-parallel to the mean magnetic field $B_0$ are
unequal. It is commonly accepted that the turbulence is driven by
(counter-)collisions between these counter-propagating wave fractions. Contrary
to this, we found a new ion-scale dynamical range of the turbulence established
by (co-)collisions among waves co-propagating in the same direction along
$B_0$. Co-collisions become stronger than counter-collisions and produce steep
non-universal spectra above certain wavenumbers dependent on the imbalance.
Spectral indexes of the strong turbulence vary around -3, such that steeper
spectra follow larger imbalances. Intermittency steepens the -3 spectra
further, up to -3.7. Our theoretical predictions are compatible with steep
variable spectra observed in the solar wind at ion kinetic scales, but further
verifications are needed by correlating observed spectra with measured
imbalances.
