  Recent data and new data analysis methods show that most probably the
parameter $w$ in the equation of state of the dark energy is smaller than -1 at
low redshifts. We briefly review some of the models with such a property and
without violating null energy condition. We investigate the difference between
the observables and predictions of these models, and how they can be explored
to single out or constrain the origin of dark energy and its properties.
