  The search of ways to generalize the theory of strong MHD turbulence for the
case of non-zero cross-helicity (or energy imbalance) has attracted
considerable interest recently. In our earlier publications we performed
three-dimensional numerical simulations and showed that some of existing models
are inconsistent with numerics. In this paper we focused our attention on
low-imbalance limit and performed new high-resolution simulations. The results
strongly suggest that in the limit of small imbalances we smoothly transition
to a standard Goldreich-Sridhar (1995) balanced model. We also claim that
Perez-Boldyrev (2009) model that predicts the same nonlinear timescale for both
components due to so-called "dynamic alignment" strongly contradicts numerical
evidence.
