  In this paper, we study the compatibility of biased domain wall scenarios
with current gravitational wave data. We show that the Cosmic Microwave
Background bounds on the fractional density of gravitational waves at the time
of decoupling may only slightly improve on the constraints that result from
requiring that domain walls never dominate the cosmic energy budget. We show
that, despite this, the range of energy scales of the domain-wall forming phase
transitions are already quite constricted, even if the networks decay early in
cosmological history. We also show that, if domain walls are to provide an
explanation to the stochastic gravitational wave background that was recently
detected by pulsar timing arrays, they not only have to decay early in the
radiation dominated era but also their energy density would have to be close to
dominating the energy density of the universe, which would require some fine
tuning of the parameters of the models.
