  We investigate the question of whether $\mathbb Q$ carries an ultrafilter
generated by perfect sets (such ultrafilters were called gruff ultrafilters by
van Douwen). We prove that one can (consistently) obtain an affirmative answer
to this question in three different ways: by assuming a certain parametrized
diamond principle, from the cardinal invariant equality $\mathfrak d=\mathfrak
c$, and in the Random real model.
  [Edit: replace "the Randor real model" with "the model obtained by adding
$\omega_1$ Cohen reals to a model of $\mathsf{CH}$, and subsequently forcing
with the Random algebra"; this is clarified in the corrigendum attached at the
end of the paper.]
