  Rotation is favorable for confinement, but a stellarator can rotate at high
speeds if and only if it is sufficiently close to quasisymmetry. This article
investigates how close it needs to be. For a magnetic field $\mathbf{B} =
\mathbf{B}_0 + \alpha \mathbf{B}_1$, where $\mathbf{B}_0$ is quasisymmetric,
$\alpha\mathbf{B}_1$ is a deviation from quasisymmetry, and $\alpha\ll 1$, the
stellarator can rotate at high velocities if $\alpha < \epsilon^{1/2}$, with
$\epsilon$ the ion Larmor radius over the characteristic variation length of
$\mathbf{B}_0$. The cases in which this result may break down are discussed. If
the stellarator is sufficiently quasisymmetric in the above sense, the rotation
profile, and equivalently, the long-wavelength radial electric field, are not
set neoclassically; instead, they can be affected by turbulent transport. Their
computation requires the $O(\epsilon^2)$ pieces of both the turbulent and the
long-wavelength components of the distribution function. This article contains
the first step towards a formulation to calculate the rotation profile by
providing the equations determining the long-wavelength components of the
$O(\epsilon^2)$ pieces.
