  We consider completely irrational nilflows on any nilmanifold of step at
least $2$. We show that there exists a dense set of smooth time-changes such
that any time-change in this class which is not measurably trivial gives rise
to a mixing nilflow. This in particular reproves and generalizes to any nilflow
(of step at least $2$) the main result proved in [AFU] for the special class of
Heisenberg (step $2$) nilflows, and later generalized in [Rav2] to a class of
nilflows of arbitrary step which are isomorphic to suspensions of
higher-dimensional linear toral skew-shifts.
