  We show that binary Toeplitz flows can be interpreted as Delone dynamical
systems induced by model sets and analyse the quantitative relations between
the respective system parameters. This has a number of immediate consequences
for the theory of model sets. In particular, we use our results in combination
with special examples of irregular Toeplitz flows from the literature to
demonstrate that irregular proper model sets may be uniquely ergodic and do not
need to have positive entropy. This answers questions by Schlottmann and Moody.
