  In a previous work with Mildenberger and Shelah, we showed that the
combinatorics of the selection hypotheses involving tau-covers is sensitive to
the selection operator used.
  We introduce a natural generalization of Scheepers' selection operators, and
show that:
  (1) A slight change in the selection operator, which in classical cases makes
no difference, leads to different properties when tau-covers are involved. (2)
One of the newly introduced properties sheds some light on a problem of
Scheepers concerning tau-covers.
  Improving an earlier result, we also show that no generalized Luzin set
satisfies U_fin(Gamma,Tau).
