  We consider the 3D Navier-Stokes system driven by an additive
finite-dimensional control force. The purpose of this paper is to show how the
approximate controllability of this system can be derived from the approximate
controllability of the Euler system linearised around some suitable trajectory.
The proof presented here is shorter than the previous ones obtained by Lie
algebraic methods and gives some new information about the structure of the
control. The dimension of the control space provided by this approach is
larger, but it is still uniform with respect to the viscosity.
