  We consider reparametrizations of Heisenberg nilflows. We show that if a
Heisenberg nilflow is uniquely ergodic, all non-trivial time-changes within a
dense subspace of smooth time-changes are mixing. Equivalently, in the language
of special flows, we consider special flows over linear skew-shift extensions
of irrational rotations of the circle. Without assuming any Diophantine
condition on the frequency, we define a dense class of smooth roof functions
for which the corresponding special flows are mixing. Mixing is produced by a
mechanism known as stretching of Birkhoff sums. The complement of the set of
mixing time-changes (or, equivalently, of mixing roof functions) has countable
codimension and can be explicitely described in terms of the invariant
distributions for the nilflow (or, equivalently, for the skew-shift), allowing
to produce concrete examples of mixing time-changes.
